Estratégias de negociação avançada de volatilidade e precificação de opções

Opção Volatilidade & amp; Preços, Estratégias e Técnicas Avançadas de Negociação.

Índice.

A linguagem das opções

Especificações do contrato.

Opção de compra: o direito de comprar ou assumir uma posição longa em um determinado ativo a um preço fixo em ou antes de um dado especificado. Opção de venda: o direito de vender ou assumir uma posição vendida em um determinado ativo.

A diferença entre uma opção e um contrato de futuros:

Um contrato de futuros requer entrega a um preço fixo. O vendedor deve fazer a entrega e o comprador deve receber o ativo. O comprador de uma opção pode optar por receber (uma chamada) ou fazer a entrega (uma opção).

O preço de exercício, ou preço de exercício, é o preço pelo qual o subjacente será entregue, caso o titular de uma opção opte por exercer o seu direito de comprar ou vender.

data de vencimento: A data após a qual a opção não poderá mais ser exercida é a data de vencimento.

O prêmio pago por uma opção pode ser separado em dois componentes, o valor intrínseco e o valor do tempo.

A quantia adicional de prêmio além do valor intrínseco que os negociantes estão dispostos a pagar por uma opção é o valor do tempo, às vezes também chamado de prêmio de tempo da opção ou valor extrínseco.

O prêmio de uma opção é sempre composto precisamente por seu valor intrínseco e seu valor de tempo. Se uma chamada de ouro de US $ 400 for negociada a US $ 50 com ouro a US $ 435 por onça, o valor de tempo da chamada deve ser de US $ 15, já que o valor intrínseco é de US $ 35. Os dois componentes devem totalizar o prêmio total da opção de US $ 50.

Se a opção não tiver valor de tempo, seu preço consistirá apenas em valor intrínseco. A opção está sendo negociada em paridade.

Qualquer opção que tenha um valor intrínseco positivo é considerada in-the-money pela quantidade do valor intrínseco. Uma opção que não tem valor intrínseco é considerada fora do dinheiro.

Uma opção cujo preço de exercício é idêntico ao preço atual do contrato subjacente é considerado no dinheiro, tal opção também está fora do dinheiro, uma vez que não tem valor intrínseco.

A distinção entre uma opção no dinheiro e uma opção fora do dinheiro, porque uma opção no dinheiro tem a maior quantidade de prêmio de tempo e geralmente é negociada de forma muito ativa.

REQUISITOS DE MARGEM.

Quando um comerciante faz uma operação de abertura em uma bolsa, a bolsa pode exigir que o comerciante deposite alguma quantia de margem ou capital de boa fé.

Estratégias Elementares.

COMPRA SIMPLES E VENDA ESTRATÉGIAS.

longo e curto um contrato subjacente.

longa uma chamada.

CARACTERÍSTICAS DE RECOMPENSA DE RISCO.

posições longas em 95, 100 e 105 chamadas.

o lucro e a perda de uma posição curta nas chamadas 95, 100 e 105.

posições longas em 95, 100 e 105 puts.

as posições de venda curtas em 95, 100 e 105 puts.

ESTRATÉGIAS DE COMBINAÇÃO.

o lucro e a perda no vencimento da compra combinada de uma chamada de 100 para 2,70 e uma de 100 para 3,70.

Curta-os.

vender um 95 colocado para 1,55 e um 105 para 1,15.

vender a chamada de 90 e comprar a chamada de 100.

compre um 105 put por 7,10 e venda um 100 put por 3,70, para um débito total de 3,40.

CONSTRUIR UM GRÁFICO DE EXPLOSÃO.

Se o gráfico se inclinar, isso será feito a um preço de exercício. Portanto, podemos calcular o proflt ou 10ss a cada preço de exercício envolvido e simplesmente conectar esses pontos com linhas retas. Se a posição for de 10 ng e números equa1 curtos de cal1s (puts), o potencial risco (upside) de subida ou recompensa será igual ao total de débito ou crédito necessário para estabelecer a posição. Se o preço de exercício for mais alto, todas as chamadas entrarão em ação, de modo que a posição inteira funcionará como uma posição subjacente que é um contrato subjacente longo ou curto igual ao número de chamadas longas ou curtas líquidas. Abaixo do preço de exercício mais baixo, todas as colocações entrarão no dinheiro, de modo que a posição inteira atuará como uma posição subjacente que seja contratos subjacentes longos ou curtos igual ao número de posições compradas ou curtas líquidas.

longa uma 95 chamada a 5,50 curto três 105 chamadas a 1,15.

short um 90 cdll em 9.35 long two 100 calls em 2.70 short four 95 puts em 1.55 long two 100 puts em 3.70.

long one 100 call a 2.70 short one 100 put em 3.70.

long one 90 put em .45 short one 100 call em 2.70 long um contrato subjacente em 99.00.

Introdução aos modelos de preços teóricos.

Se ele compra opções, não só ele deve estar certo sobre a direção do mercado, ele também deve estar certo sobre a velocidade do mercado.

Os fatores mínimos que você deve considerar:

O preço do contrato subjacente. O preço de exercício A quantidade de tempo restante até a expiração. A direção na qual ele espera que o mercado subjacente se mova. A velocidade na qual ele espera que o mercado subjacente se mova.

VALOR TEÓRICO.

As duas considerações mais comuns em um investimento financeiro são o retorno esperado e os custos de manutenção. E, de fato, os dividendos são uma consideração adicional na avaliação de opções em estoque.

O objetivo da avaliação de opções é determinar, através do uso de modelos teóricos de precificação, o valor teórico de uma opção. O comerciante pode, então, tomar uma decisão inteligente sobre se a opção é superfaturada ou subvalorizada no mercado, e se a avaliação teórica é suficiente para justificar a entrada no mercado e a realização de uma negociação.

UMA ABORDAGEM SIMPLES.

Podemos agora resumir os passos necessários no desenvolvimento de um modelo:

Proponha uma série de preços possíveis no vencimento do contrato subjacente. Atribuir uma probabilidade apropriada a cada preço possível. Manter um mercado subjacente livre de arbitragem. A partir dos preços e probabilidades nos passos 1, 2 e 3, calcule o retorno esperado para a opção. A partir do retorno esperado da opção, deduzir o custo de carregamento.

Em sua forma original, o Modelo Black-Scholes pretendia avaliar as opções européias (sem exercício antecipado permitido) sobre ações pagas sem dividendos. Pouco depois de sua introdução, percebendo que as ações mais vantajosas pagam dividendos, Black e Scholes acrescentaram uma quantia de dividendos. Em 1976, Fischer Black realizou pequenas modificações no modelo para permitir a avaliação de opções sobre contratos futuros. E em 1983, Mark Garman e Steven Kohlhagen fizeram várias outras modificações para permitir a avaliação de opções em moedas estrangeiras. A versão de futuros e a versão em moeda estrangeira são conhecidas oficialmente como o Modelo Preto e o Modelo Garman-Kohlhagen, respectivamente. Mas o método de avaliação em cada versão, seja o modelo Black-Scholes original para opções de ações, o modelo Black para opções de futuros ou o modelo Garman-Kohlhagen para opções em moeda estrangeira, é tão semelhante que todos passaram a ser conhecidos como simplesmente o modelo Black-Scholes. As várias formas do modelo diferem principalmente em como eles calculam o preço a termo do contrato subordinado, e um operador de opções simplesmente escolherá a forma apropriada para o instrumento subjacente.

Para calcular o valor teórico de uma opção usando o modelo de Black-Scholes, precisamos conhecer no mínimo cinco características da opção e seu contrato subjacente. Tem:

O preço de exercício da opção. A quantidade de tempo restante até a expiração. O preço atual do contrato subjacente. A taxa de juros livre de risco ao longo da vida da opção. A volatilidade do contrato subjacente.

Black e Scholes também incorporaram em seu modelo o conceito de hedge sem risco. Para tirar proveito de uma opção teoricamente incorreta, é necessário estabelecer um hedge compensando a posição da opção com essa posição subjacente teoricamente equivalente. Ou seja, qualquer que seja a posição de opção que tomemos, devemos assumir uma posição de mercado oposta no contrato subjacente. A proporção correta de contratos subjacentes necessários para estabelecer esse hedge sem risco é conhecida como hedge ratlo.

Volatilidade.

Passeios aleatórios e distribuições normais.

Isso leva a uma importante distinção entre a avaliação de um contrato subjacente e a avaliação de uma opção. Se assumirmos que os preços são distribuídos ao longo de uma curva de distribuição normal, o valor de um contrato subjacente depende de onde o pico da curva está localizado, enquanto o valor de uma opção depende da rapidez com que a curva se espalha.

DISTRIBUIÇÕES LOGNORMAIS.

Uma taxa de retorno continuamente composta de + 12% gera um lucro de US $ 127,50 após um ano, enquanto uma taxa continuamente composta de retorno de -12% produz uma perda de apenas US $ 113,08.

Quando se pressupõe que as variações de preço sejam normalmente distribuídas, a composição contínua dessas variações de preço fará com que os preços no vencimento sejam distribuídos lognormalmente.

O modelo Black-Scholes é um modelo de tempo contínuo. Assume-se que a volatilidade de um instrumento subjacente é constante ao longo da vida da opção, mas que essa volatilidade é continuamente combinada. Estas duas suposições significam que os possíveis preços do instrumento subjacente no vencimento da opção são lognormalmente distribuídos.

Também explica porque é que as opções com preços de exercício mais elevados têm mais valor do que as opções com preços de exercício mais baixos, em que ambos os preços de exercício parecem ser uma quantia idêntica à do preço do instrumento subjacente.

Resumir as asserções mais importantes que regem o movimento de preços no modelo de Black-Scholes:

Mudanças no preço de um instrumento subjacente são randornadas e não podem ser manipuladas artificialmente, nem é possível prever antecipadamente a direção na qual os preços se moverão. As alterações percentuais no preço de um instruente subjacente são distribuídas mensalmente. Como as mudanças percentuais no preço do instruente subjacente são assumidas como sendo contínuas, os preços do instrumento subjacente na expiração serão lognormalmente distribuídos. A média da distribuição lognormal será localizada ao preço a termo do contrato subjacente.

TIPOS DE VOLATILIDADES

Volatilidade Futura: A volatilidade futura é o que todo trader gostaria de saber, a volatilidade, na melhor das hipóteses, descreve a futura distribuição de preços para um contrato subjacente. Previsão de Volatilidade Histórica Volatilidade Volatilidade Implícita: Está a ser implícita a volatilidade do contrato subjacente através do preço da opção no mercado. Embora o termo prêmio realmente se refira ao preço de uma opção, é comum entre os traders se referir à volatilidade implícita como o nível de prêmio ou prêmio. Se a atual volatilidade implícita é alta por padrões históricos, ou alta em relação à recente volatilidade histórica do contrato subjacente, um trader pode dizer que os níveis de prêmio são altos; se a volatilidade implícita é incomumente baixa, ele pode dizer que os níveis de prêmio são baixos.

Ele poderia então examinar a diferença entre o valor teórico de cada opção e seu preço em vender quaisquer opções que fossem superfaturadas em relação ao valor teórico, e comprar quaisquer opções que estivessem subvalorizadas.

Usando o valor teórico de uma opção.

A compra ou venda de uma opção teoricamente incorreta nos obriga a estabelecer um hedge, adotando uma posição oposta no contrato subjacente. Quando isso é feito corretamente, para pequenas mudanças no preço do subjacente, o aumento (diminuição) no valor da posição de otimização irá compensar exatamente a diminuição (aumento) no valor da posição oposta no contrato subjacente. Tal hedge é imparcial, ou neutro, quanto à direção do contrato subjacente.

O número que nos permite estabelecer um hedge neutro nas condições atuais de mercado é um subproduto do modelo teórico de precificação e é conhecido como o índice de hedge ou, mais comumente, o delta.

O delta de uma opção de chamada está sempre entre 0 e 1,00. O delta de uma opção pode mudar à medida que as condições do mercado mudam. Um contrato subjacente sempre tem um delta de 1,00.

Os passos que tomamos até agora ilustram o procedimento correto ao usar um valor teórico de opção:

Compra (venda) opções subvalorizadas (supervalorizadas). Estabeleça uma cobertura delta neutra contra o contrato subjacente. Ajuste a cobertura em intervalos regulares para permanecer em delta neutro.

Nesse momento, pretendemos fechar a posição por:

Deixar qualquer opção fora do dinheiro expirar sem valor. Vender quaisquer opções dentro do dinheiro em paridade (valor intrínseco) ou, equivalentemente, exercê-las e compensá-las com o contrato futuro subjacente. Atribuir quaisquer contratos futuros pendentes ao preço de mercado.

Em um mercado sem atrito, assumimos que:

Os negociadores podem livremente comprar ou vender o contrato subjacente sem restrições. Todos os comerciantes podem emprestar e emprestar dinheiro à mesma taxa. Os custos de transação são zero. Não há considerações tributárias.

Valores de opção e condições de mercado em mudança.

três interpretações do delta:

O índice de hedge Taxa de variação no valor teórico: O de1ta é uma medida de como o valor de uma opção muda em relação a uma alteração no preço do contrato subjacente. Posição Subjacente Teórica ou Equivalente.

O gama, às vezes referido como a curvatura de uma opção, é a taxa na qual o delta de uma opção é alterado conforme o preço das alterações subjacentes.

Se uma opção tiver um gamrna de 5 para cada aumento de ponto (fal1) no preço do und. erlying, a opção ganhará (perde) 5 de1tas.

Todo operador de opções aprende a olhar com cuidado não só o risco direcional atual (o delta), mas também como esse risco direcional mudará se o mercado subjacente começar a se mover (o gama).

O teta (θ) ou o fator de decaimento do tom é a taxa na qual uma opção perde valor à medida que o tempo passa.

O VEGA OU KAPPA.

A vega de uma opção é geralmente dada em mudança de ponto com valor teórico para cada mudança de um ponto percentual na volatilidade.

Como vega não é uma letra grega, uma alternativa comum na literatura acadêmica, onde letras gregas são preferidas, é kappa (K).

A sensibilidade do valor teórico de uma opção a uma mudança nas taxas de juros é dada pelo seu rho (P).

Delta: Os deltas variam de zero para chamadas out-of-the-money até 100, para chamadas com muito dinheiro, e de zero para patamares muito fora do dinheiro, para -100, para fundos profundamente in-the-money. puts.

As chamadas no dinheiro têm deltas de aproximadamente 50, e no dinheiro coloca aproximadamente -50.

À medida que o tempo passa, ou à medida que diminuímos nossa hipótese de volatilidade, chamamos os deltas de afastar-se de 50, e coloca os deltas fora de -50. À medida que aumentamos nossa hipótese de volatilidade, os deltas cal1 avançam para 50 e colocam deltas em direção a -50.

À medida que aumentamos nossa suposição de volatilidade, a gama de um in.

opção de dinheiro sobe, enquanto gama de um at le.

opção de dinheiro cai. À medida que diminuímos nossa hipótese de volatilidade, ou conforme o tempo de expiração fica mais curto, a gama de um in.

a opção de dinheiro cai, enquanto a gama de um at.

a opção do dinheiro aumenta, às vezes dramaticamente.

opções de dinheiro têm maior etas do que em.

das opções de dinheiro com especificações contratuais idênticas.

O teta de uma opção no dinheiro aumenta como abordagens de vencimento. Uma opção de curto prazo, no dinheiro, vai decair mais rapidamente do que uma opção de longo prazo, com dinheiro.

À medida que aumentamos (diminuímos) nossa hipótese de volatilidade, o teta de uma opção aumentará (queda). Volatilidade mais alta significa que há um valor de tempo maior associado à opção, de modo que, no decaimento de cada dia, também será maior quando nenhum movimento ocorrer.

As opções out-of-the-money têm a maior vega como aperitivo de valor teórico.

As várias posições e seus respectivos signos são dados na Figura 6-26. O sinal do delta, gama, teta ou vega, associado à magnitude dos números, tel1 o comerciante que muda nas condições de mercado vai ajudar ou prejudicar sua posição, e em que grau. O efeito positivo ou negativo de mudanças nas condições de mercado é resumido na Figura 6-27.

A elasticidade de uma opção, às vezes denotada com a letra grega omega (ou menos comumente a letra grega lambda), é a variação percentual relativa no valor de uma opção para uma determinada mudança percentual no preço do contrato subjacente.

A elasticidade é por vezes referida como o valor de alavancagem da opção. Quanto maior a elasticidade de uma opção, maior será a alavancagem da opção.

Um método fácil de calcular:

elasticidade = (preço subjacente) / (valor teórico) * delta.

Introdução ao Spreading.

A disseminação é simplesmente uma forma de permitir que um operador de optlon tire proveito de opções teoricamente mal calculadas, enquanto ao mesmo tempo reduz os efeitos de mudanças de curto prazo nas condições do mercado, de modo que ele possa seguramente manter uma posição de optlon à maturidade.

Por que espalhar?

Em algum momento, o operador inteligente terá que considerar não apenas o lucro potencial, mas também o risco associado a uma estratégia.

Nenhum trader sobreviverá por muito tempo se seu sustento depender de estimar cada entrada com 100% de precisão. Mesmo quando ele estima incorretamente os insumos, o profissional experiente pode sobreviver se tiver construído estratégias inteligentes de dispersão que permitam uma ampla margem de erro.

Volatilidade se espalha.

Independentemente do método que escolhermos, cada spread terá certas características em comum:

Cada spread será aproximadamente delta neutro. Cada spread será sensível a alterações no preço do instrumento subjacente. Cada spread será sensível a mudanças na volatilidade implícita. Cada propagação será sensível à passagem do tempo.

BACKSPREAD.

Um backspread é um spread delta neutro que consiste em opções mais longas (compradas) do que opções curtas (vendidas), em que todas as opções expiram ao mesmo tempo.

Um backspread de chamadas consiste em chamadas longas com um preço de exercício mais alto e chamadas curtas a um preço de exercício mais baixo. Um backspread de venda consiste em valores comprados a um preço de exercício mais baixo e pon - tos curtos a um preço de exercício mais alto.

Se nenhum movimento ocorrer, um backspread provavelmente será uma estratégia perdida.

Um trader tenderá a escolher o tipo de spread que reflete sua opinião sobre a direção do mercado. Se ele prevê um mercado com grande potencial de valorização, tenderá a escolher um call backspread; se ele prevê um mercado com grande potencial de desvantagem, tenderá a escolher um substituto. Ele evitará recuos em mercados silenciosos, já que é improvável que o contrato subjacente se mova muito em qualquer direção.

SPREAD VERTICAL DA RELAÇÃO.

Um comerciante que leva o lado oposto de um backspread também tem um spread neutro delta, mas ele é mais curto do que os contratos longos, com todas as opções expirando ao mesmo tempo. Esse spread é, às vezes, chamado de spread proporcional ou spread vertical.

Designe o oposto de um backspread como um spread vertical de proporção.

Um straddle consiste em uma chamada longa e uma put longa, ou uma chamada curta e uma put curta, em que ambas as opções têm o mesmo preço de exercício e vencem ao mesmo tempo.

Se tanto o call quanto o put forem comprados, o trader é dito ser longo o straddle; Se ambas as opções forem vendidas, o comerciante é dito ser curto o straddle.

Como um straddle, um strangle consiste em uma call longa e uma put longa, ou uma call curta e uma put curta, onde ambas as opções expiram ao mesmo tempo. Em um estrangulamento, no entanto, as opções têm preços de exercício diferentes. Se ambas as opções são compradas, o comerciante é longo o estrangulamento se ambas as opções são vendidas, o comerciante é curto o estrangulamento.

Para evitar confusão, normalmente se considera que um estrangulamento consiste em opções fora do dinheiro. Se o mercado subjacente estiver atualmente em 100 e um comerciante quiser comprar o estrangulamento em junho de 95/105, presume-se que ele quer comprar uma ligação de junho de 95 e uma de junho de 105. Quando ambas as opções estão dentro do dinheiro, a posição é por vezes referida como uma coragem.

Uma borboleta consiste em opções em três preços de exercício igualmente espaçados, onde todas as opções são do mesmo tipo (todas as chamadas ou todas as opções) e expiram ao mesmo tempo.

Em uma longa borboleta os preços de exercícios externos são comprados e o preço de exercício é menor, e vice-versa por uma borboleta curta.

É sempre 1 x 2 x 1, com dois de cada preço de exercício transaccionado por cada um dos preços externos praticados. Se a proporção for diferente de 1 x 2 x 1, o spread não é mais uma borboleta.

uma borboleta longa tende a agir como uma relação vertica1 espalhada e uma borboleta curta tende a agir como um backspread.

TIME SPREAD (spread do calendário ou spread horizontal)

Os spreads de tempo, às vezes chamados de spreads de calendário ou spreads horizontais, consistem em posições opostas que expiram em meses diferentes. O tipo mais comum de propagação de tempo consiste em o.

O tipo mais comum de spread de tempo consiste em posições opostas em duas opções do mesmo tipo (ou ambas as chamadas ou ambas as opções), em que ambas as opções têm o mesmo preço de exercício. Quando a opção de longo prazo é comprada e a opção de curto prazo é vendida, um comerciante é longo o tempo de propagação; quando a opção de curto prazo é comprada e a opção de longo prazo é vendida, o comerciante é curto o tempo se espalhou.

Se assumirmos que as opções que compõem um spread de tempo estão aproximadamente no dinheiro, os spreads de tempo têm duas características importantes:

Um spread de longo tempo sempre quer que o mercado subjacente fique parado. Como uma opção de curto prazo no dinheiro sempre se deteriora mais rapidamente do que uma opção de longo prazo no dinheiro, independentemente de as opções serem chamadas ou opções, tanto um longo intervalo de tempo de chamada quanto um longo tempo de espera querem o subjacente. mercado para se sentar sti1l. O ideal é que ambos os spreads desejem que a opção de curto prazo expire no dinheiro, de modo que a opção de longo prazo retenha o máximo de valor possível, enquanto a opção de curto prazo expira sem valor.

Um spread de longo prazo sempre se beneficia de um aumento na volatilidade implícita. À medida que o tempo de expiração aumenta, a vega de uma opção aumenta. Isso significa que uma opção de longo prazo é sempre mais sensível no total de pontos a uma mudança na volatilidade do que uma opção de curto prazo com o mesmo preço de exercício.

Essas duas forças opostas, a queda no valor de uma opção devido à passagem do tempo e a mudança no valor de uma opção devido a mudanças na volatilidade, propiciam que o tempo se espalhe por suas características indevidas. Quando um comerciante compra ou seleciona um spread de tempo, ele não está apenas tentando prever o movimento no mercado subjacente. Ele está tentando prever mudanças na volatilidade imposta.

O EFEITO DA ALTERAÇÃO DAS TAXAS DE JUROS E DOS DIVIDENDOS.

Se estivermos considerando opções de ações com datas de vencimento diferentes, consideraremos dois preços futuros diferentes. E esses dois preços a termo podem não ser igualmente sensíveis a uma mudança nas taxas de juros.

Se as taxas de juros aumentarem, o spread de tempo aumentará porque o preço a termo de junho subirá mais rapidamente do que o preço a termo de março. Portanto, um spread de tempo de chamada longo (curto) no mercado de opções de ações deve ter um rho positivo (negativo).

se as taxas de juros aumentarem, o spread de tempo de venda diminuirá. Portanto, um spread longo (curto) de tempo de colocação no mercado de opções de ações deve ter um rho negativo (positivo).

Um aumento (redução) nos dividendos diminui (eleva) o preço a termo das ações.

Em um spread de tempo, se um pagamento de dividendo for esperado entre o vencimento da opção de curto e longo prazo, a opção de longo prazo será afetada pelo preço de baixa da ação. Assim, um aumento nos dividendos, se pelo menos um pagamento de dividendo for esperado entre as datas de vencimento, fará com que os spreads de tempo de chamada sejam limitados e os spreads de tempo aumentem. Um decréscimo nos dividendos terá o efeito oposto, com o alargamento dos spreads de call time e o estreitamento dos spreads de tempo. O efeito da alteração das taxas de juros e dividendos sobre os spreads de opções de ações é mostrado abaixo:

SPREADS DIAGONAIS.

Um spread diagonal é semelhante a um spread de tempo, exceto que as opções têm preços de exercício diferentes.

OUTRAS VARIAÇÕES.

Uma árvore de Natal (também chamada de ladd é um termo que pode ser aplicado a uma variedade de spreads. O spread geralmente consiste em três preços de exercício diferentes, onde todas as opções são do mesmo tipo e expiram ao mesmo tempo. (short) ligue para a árvore de Natal, uma chamada é comprada (vendida) pelo menor preço de exercício, e uma chamada é vendida (comprada) em cada um dos preços de exercício mais altos. Em uma árvore de natal longa (curta), um put é comprado (vendido) pelo maior preço de exercício, e um put é vendido (comprado) em cada um dos preços de exercício mais baixos.

Árvores de Natal longas, quando feitas em delta neutro, podem ser vistas como tipos particulares de spreads verticais de proporção. Tais spreads, portanto, aumentam de valor se o mercado subjacente ficar parado ou se mover muito lentamente. Árvores de Natal curtas podem ser vistas como tipos específicos de encostas e, portanto, aumentam o valor com grandes movimentos no mercado subjacente.

É possível construir um spread que tenha as mesmas características de uma borboleta comprando straddle (strangdle) e vendendo strangle (straddle) onde o straddle é executado a um preço de exercício entre os preços de exercício do strangle. Todas as opções devem expirar ao mesmo tempo. Porque a posição quer o mesmo resultado que uma borboleta, é conhecida como uma borboleta de ferro.

Outra variação em uma borboleta, conhecida como condor, pode ser construída dividindo-se os preços de exercício internos. Agora a posição consiste em quatro opções em preços de exercício consecutivos onde as duas opções externas são compradas e as duas opções internas vendidas (um longo condor), ou as duas opções internas são compradas e as duas opções externas vendidas (um condor curto). Como com uma borboleta, todas as opções devem ser do mesmo tipo (todas as chamadas ou todas as opções) e expirar ao mesmo tempo.

ESPALHE SENSIBILIDADES.

ESCOLHA DE UMA ESTRATÉGIA APROPRIADA.

Com tantos spreads disponíveis, como sabemos qual é o melhor tipo de spread?

Idealmente, gostaríamos de construir um spread comprando opções que estão subvalorizadas e estabelecendo opções que são superfaturadas.

Se as opções gerais / y parecerem underprtced (baixa volatilidade implícita), procure spreads com uma vega positiva. Isso inclui estratégias na categoria backspread ou spread de longo prazo. Muitas vezes, as opções parecem superestimadas (alta volatilidade implícita), procurando spreads com uma vega negativa. Isso inclui estratégias na categoria de proporção de spread vertical ou curto.

É provável que os spreads de longo prazo sejam lucrativos quando a volatilidade implícita é baixa, mas espera-se que aumente; spreads curtos são prováveis ​​de serem rentáveis ​​quando a volatilidade implícita é alta, mas espera-se que ela falhe.

AJUSTES

O uso otimizado de um modelo teórico de precificação requer que um negociante mantenha continuamente uma posição neutra durante a vida útil do spread.

Ajuste em intervalos regulares & # x2013; Em teoria, o processo de ajuste é assumido como contínuo porque a volatilidade é considerada uma medida contínua da velocidade do mercado. Ajuste quando a posição se torna um número predeterminado de 01 delta ou curto. Ajuste por sensação.

ENTRANDO EM UMA ORDEM DE SPREAD.

As seguintes ordens de contingência, todas definidas no Apêndice A, são frequentemente utilizadas nos mercados de opções:

Imediato ou Cancelar.

Mercado se tocado.

Mercado No Fim.

Um cancela o outro.

Parar a ordem de envio.

Ordem de Stop Loss.

Considerações sobre Risco.

ESCOLHENDO O MELHOR SPREAD.

Podemos resumir esses riscos da seguinte forma:

Risco Delta (DirectionaI) - O risco de o mercado subjacente se mover em uma direção e não em outra. Quando criamos uma posição que é delta neutra, estamos tentando assegurar que inicialmente a posição não tenha preferência particular quanto à direção na qual o instrumento subjacente se moverá. Uma posição neutra delta não elimina necessariamente todo o risco direcional, mas geralmente nos deixa imunes a riscos direcionais dentro de uma faixa limitada. Gama (Curvatura) Risco - O risco de um grande movimento no contrato subjacente, independentemente da direção. A posição gama é uma medida da sensibilidade de uma posição a movimentos tão grandes. Uma posição gama positiva não possui risco gama, já que tal posição, em teoria, aumentará em valor com o movimento no contrato subjacente. Uma posição gama negativa, no entanto, pode rapidamente perder sua vantagem teórica com um grande movimento no contrato subjacente. As conseqüências de tal movimento devem sempre ser consideradas quando se analisam os méritos relativos de posições diferentes. Risco Theta (Decaimento do Tempo) 一 Therisk que o tempo passará sem nenhum movimento no contrato subjacente. Este é o lado oposto do risco gama. Posições com gama positiva se tornam mais valiosas com grandes movimentos no subjacente. Mas se o movimento ajuda, a passagem do tempo dói. Um gamma positivo sempre anda de mãos dadas com um theta negativo. Um negociante com uma teta negativa terá sempre que considerar o risco em termos de quanto tempo pode passar antes que a margem teórica do spread desapareça. A posição quer movimento, mas se o movimento não ocorrer no dia seguinte, ou na próxima semana, ou no próximo mês, será divulgado, em teoria, ainda será rentável? Risco Vega (Volatilidade) & # x2014; O risco de que a volatilidade que introduzimos no modelo teórico de precificação esteja incorreta. Se inserirmos uma volatilidade incorreta, estaremos assumindo uma distribuição incorreta dos preços subjacentes ao longo do tempo. Uma vez que algumas posições têm uma vega positiva e são prejudicadas pela volatilidade decrescente, e algumas posições têm uma vega negativa e são prejudicadas pelo aumento da volatilidade, a vega representa um risco para todas as posições. Um negociador deve sempre considerar quanto a volatilidade pode se mover contra ele antes que o lucro potencial de uma posição desapareça. Rho (Taxa de juros) Risco - O risco de que as taxas de juros mudem ao longo da vida da opção. Uma posição com rho positivo será ajudada (prejudicada) por um aumento (declínio) nas taxas de juros, enquanto uma posição com rho negativo1 mostrará apenas as características opostas. Geralmente, a taxa de juros é o menos importante dos dados em um modelo teórico de precificação, e é improvável, exceto em situações especiais, que um trader pense extensivamente no risco associado a uma posição.

CONSIDERAÇÕES PRÁTICAS.

Embora não haja substituto para a experiência, a maioria dos traders rapidamente aprende uma regra importante: straddles e estrangulamentos são os mais arriscados de todos os spreads.

QUANTA MARGEM POR ERRO?

Talvez a melhor maneira de abordar a questão seja perguntar não qual é a margem razoável de erro, mas perguntar qual é o tamanho correto para fazer um spread, dada uma margem conhecida para erro.

DIVIDENDOS E INTERESSES.

O QUE É UM BOM SPREAD?

É impossível levar em consideração todos os riscos possíveis. Um spread que passasse em todos os testes de risco provavelmente teria tão pouca margem teórica que não valeria a pena. Mas o comerciante que se permite uma margem razoável para o erro descobrirá que mesmo suas perdas não levarão à ruína financeira. Um bom spread não é necessariamente aquele que mostra o maior lucro quando as coisas correm bem; pode ser o que mostra a menor perda quando as coisas correm mal. As negociações vencedoras sempre cuidam de si mesmas. Negociações perdedoras, que não trazem de volta todos os lucros dos vencedores, são igualmente importantes.

AJUSTES

Um ajuste na posição delta do negociador pode reduzir seu risco direcional, mas se ele simultaneamente aumenta seu risco gama, teta ou vega, ele pode inadvertidamente estar trocando um tipo de risco por outro.

Um ajuste delta feito com o contrato subjacente é essencialmente um ajuste de risco neutro. Um ajuste feito com opções pode reduzir o risco de delta, mas também mudará as outras características associadas à posição.

Um operador disciplinado sabe que às vezes, por causa de considerações de risco, o melhor caminho é reduzir o tamanho do spread, mesmo que isso signifique aumentar a vantagem teórica. Isso pode ser difícil para o ego do negociante, especialmente se ele deva voltar pessoalmente ao mercado e comprar de volta as opções que ele originalmente vendeu a um preço mais baixo ou vender as opções que comprou originalmente a um preço mais alto. No entanto, se um comerciante não estiver disposto a engolir seu orgulho de tempos em tempos, e admitir que cometeu um erro, sua carreira comercial certamente será curta.

If a trader finds that any de1ta adjustment in the option market that reduces his risk will also reduce his theoretical edge，and he is unwil1ing to give up any theoretical edge, his only recourse is to make h1s adjustments in the underlying market. An underlying contract has no gamma, theta, or vega, so the risks of the position will remain essentially the same.

A QUESTION OF STYLE.

In practice, however, many option traders begin theîr trading careers by taking positions in the underlying market, where direction is the primary consideration. Many traders therefore deve10p a style of trading based on presumed directional moves in the underlying market. A trader might，for examp1e, be a trend follower, adhering to the philosophy that "the trend is your friend." Or he might be a contrarian. preferring to "buy weakness, sell strength."

An important consideration in deciding whether to enter into a trade is often the ease with which the trader can reverse the trade. Luid option markets, where there are many buyers and sellers, are much less risky than illuid markets, where there are few buyers and sellers. In the same way, a spread which consists of very luid options is much less risky出ana spread which consists of one or more illuid options.

Bull and Bear Spreads.

NAKED POSITIONS.

If all options are overpríced (high implied volatility), we might sell puts to create a bullish position, or sel1 calls to create a bearish position. If al1 options are underpriced (low implied volatility), we might buy calls ωcreate a bullish position, or buy puts to create a bearish position.

The problem with this approach is that，as with all non-hedged positions, there is very llttle margin error.

BULL AND BEAR RATIO SPREADS.

If a trader believes that implied volatility is too hlgh, one sensible strategy is a ratio vertical spread.

Even though the trader was correct ín his bullish sentiment, the position was primarily a volatility spread, so that the volatility characteristics of the position eventually outweighed any considerations of market direction.

Since this spread is a volatility spread, the primary consideration, as before, is the volatility of the market. Only secondarily are we concerned with the direction of movement. If the trader overestimates volatility, and the market moves more slowly than expected, the spread which was initially de1ta positive can instead become delta negative.

BULL AND BEAR BUTTERFLIES AND TlME SPREADS.

If the underlying market is currently at 100, he might choose to buy the June 105/110/115 call butterfly. Since this position wants the underlying market at 110 at expiration, and it is currently at 100, the position is a bull butterfly. This will be reflected in the position having a positive delta.

Unfortunately, if the underlying market moves too swift1y, say to 120, the butterfly can invert from a positive to a negative delta position.

Conversely, if the trader is bearish, he can always choose to buy a butterfly where the inside exercise price is below the current price of the underlying market. But again, if the market moves down too quickly and goes through the inside exercise price, the position will invert from a negative to a positive delta.

In a simi1ar manner, a trader can choose time spreads 由atare either bul1ish or bearish. A long time spread always wants the near-term contract to expire exactly at-the-money. A long time spread will be initial1y bullish if the exercise price of the time spread is above the current price of the underly1ng market.

SPREADS VERTICAIS.

Vertical spreads are not on1y initially bullish or bearish, but they remain bullish or bearish no matter how market conditions change. A vertical spread always consists of one long (purchased) option and one short (sold) option, where both options are of the same type (either both calls or both puts) and expire at the same time. The options are distinguished only by their different exercise prices. Typical vertical spreads might be:

buy 1 June 100 call.

sell 1 June 105 cal1.

buy 1 March 105 put.

sell 1 March 95 put.

If a trader wants to do a vertical spread, he has essentially four choices. If he is bullish he can choose a bull vertical call spread or a bull vertical put spread; if he is bearish he can choose a bear vertical call spread or a bear vertical put spread. Por exemplo:

bull call spread: buy a June 100 call.

bull put spread: buy a June 100 put.

bear call spread: sell a June 100 call.

bear put spread: sell a June 100 put.

Two factors determine the total directional characteristlcs of a vertlcal spread:

The delta of the specific vertical spread The size in which the spread is executed.

The greater the distance between exercise prices, the greater the delta value associated with the spread. A 95/110 bull spread wil1 be more bullish than a 100/110 bull spread, which will, ín turn, be more bullish than a 100/105 bull spread.

Once a trader decides on an expiratlon month in which to take his directlonal position, he must decide which specific spread is best. Ou seja, ele deve decidir quais preços de exercício usar. A common approach is focus on the at-the-money optlons. If a trader does this, he will have the fol1owing choices:

The reason becomes clear if we recall one of the characteristics of option evaluation introduced in Chapter 6: If we consider three options, an in-the-money， at-the-money， and out-of-the-money option which are identical except for their exercise prices, the at-the-money option is always the most sensitive in total points to a change in volatility.

This characteristic leads to a very simple rule for choosing bull and bear vertical spreads:

If implied volatility is too low, vertical spreads should focus on purchasing the at-the-money optlon. If implied volatility is too high, vertical spreads should focus on selling the at-the-money options.

A trader is not required to execute any vertical spread by first buying or selling the at-the-money option. Such spreads always involve two options, and a trader can choose to either execute the complete spread in one transaction, or leg into the spread by trading one option at a time. Regardless of how the spread is executed, the trader should focus on the at-the-money option, either buying it when implied volatility is too low, or selling it when implied volatility is too high.

The choice of the at-the-money option is slightly different when we move to stock options. If we define the at-the-money option as the one whose de1ta is closest to 50, then we may find at the at-the-money option is not always the one whose exercise price is closest current price of the underlying contract. This ís because the option with a delta closest 50 will be the one whose exercise price ís closest to forward price of underlying contract. In stock options, the forward price is the current price of stock, plus carrying costs on the stock, less expected dividends.

Why míght a trader with a directional opinion prefer a vertical spread to an outright long or short posítíon in the underlying instrument? For one thing, a vertical spread is much less risky than an outright posítion. Atrader who wants to take a position which is 500 deltas long can either buy fíve underlying contracts or buy 25 vertical calI spreads with a delta of 20 each. The 25 vertical spreads may sound riskier than five underlying contracts, until we remember at a vertical spread has limited risk whíle the position in underlying has open-ended risk. Of course, greater risk also means greater reward. A trader with a long or short position in the underlyíng market can reap huge rewards if the market makes a large move in his favor. By contrast, the vertical spreader's profits are limited, but he will also be much less bloodied if the market makes an unexpected move in the wrong direction.

Option Arbitrage.

SYNTHETIC POSITIONS.

synthetic long underlying = long call + short put synthetic short underlying = short call + long put.

where all options expire at the same time and have the same exercise price.

Rearranging the components of a synthetic underling position, we can create four other synthetic relationships:

synthetic long call = long an underlylng contract + long put synthetic short call = short an underlying contract + short put synthetic long put = short an underlying contract + long call synthetic short put = long an underlying contract + short call.

The difference between the call and put price ís often referred to as the synthettc market. In the absence of any interest or dividend considerations, the value of the synthetic market can be expressed as:

call price - put price = underlying price - exercise price.

If this equality holds, there ís no difference between taking a position in the underlying market, or taking an equivalent synthetic position in the option market.

The three-sided relationship between a call, a put, and its underlying contract means that we can always express the value of any one of these contracts in terms of the other two:

underlying price = call prîce - put prîce + exercíse price call prîce = underlying price + put príce - exercíse price put price = call prîce - underlying prîce + exercise price.

This three-sided relationship is sometimes referred put-call parity .

CONVERSIONS AND REVERSALS.

When a trader identifies two contracts which are essentially the same but which are trading at different prices, the natural course ís to execute an arbitrage by purchasing the cheaper contract and selling the more expensive.

No matter what happens in the underlying market, the underlying position will do exactly .25 better than the synthetìc position. The entire position wíll therefore show a profit of .25, regardless of movement in the underlying market.

The foregoing position, where the purchase of an underlying contract is offset by the sale of a synthetic position, is known as a conversion . The opposíte position, where the sale of an underlying contract is offset by the purchase of a synthetic position, is known as a reverse conversion or, more commonly, a reversal .

conversion = long underlying + synthetlc short underlying = long underlying + short call + long put reversal = short underlying + synthetic long underlying = short underlying + long call + short put.

As before, we assume that the call and the put have the same exercise price and expiration date.

Typically, an arbitrageur will attempt to simultaneously buy and sell the same items in different markets to take advantage of price discrepancies between the two markets.

Synthetic positions are often used to execute conversions and reversals, so traders sometimes refer to the synthetic market (the difference between the call price and put price) as the converston/reversal market.

All experienced traders are familiar with the price relationship between a synthetic position and its underlying contract, so that any imbalance in the conversion/reversal market is 1ikely to be short-lived. If the synthetic is overpriced, all traders will want to execute a conversion (buy the underlying, sell the call, buy the put). If the synthetic is underpriced, all traders will want to execute a reversal (sell the underlying, buy the call, sell the put). Such activity, where everyone is attempting to do the same thing, will quickly force the synthetic market back to equilibrium. De fato, os desequilíbrios no mercado de conversão / reversão são geralmente pequenos e raramente duram mais do que alguns segundos.

Futures Option Markets.

If the cash flow resulting from an option trade and a trade in the underlying instrument is identical, the synthetic relationship is simply:

call price - put price = underlying price - exercise price.

This will be true if interest rates are zero, or in futures markets where both the underlying contract and options on that contract are subject to futures-type settlement.

Assuming that all options are European (no early exercise permitted), we can now express the synthetic relationship in futures markets where the options are settle in cash as follows:

cal1 price - put price = futures price - exercise price - carrying costs.

where the carrying costs are calculated on either the difference between the futures price and the exercise price, or the difference between the call price and put price, both of which will be approximately the same.

Taking into consideration the interest rate component, we can express the synthetic relationship as:

call price - put price = stock price - exercise price + carrying costs.

where the carrying costs are calculated on the exercise price.

call price - put price = stock price - exercise price + carrying costs - dividends.

where the carrying costs are calculated on the exercise price and the dividends are those expected prior to expiration.

ARBITRAGE RISK.

Risco da taxa de juros.

Anytime a strategy is executed one leg at a time, there is always the risk of an adverse change in prices before the strategy can be completed.

The practical solution is to avoid carrying conversions and reversals to expiration when there is a real possibility of expiration right at the exercise price.

If al1 contracts are subject to futures-type settlement, any credit or debit resulting from changes in the price of the underlying futures contract wil1 be offset by an equal but opposite cash flow from changes in prices of the option contracts.

The risk arises because a synthetic position in options and an actual position in the underlying contract can have different characteristics， either in terms of settlement procedure, as in the futures option market, or in terms of the dividend payout, as in the stock option market.

How might we eliminate this risk?

short a call long a put long an underlying contract.

replace the long underlyingpositlon with a deeply in-the-money call Now our position is:

short a call long a put long a deeply in-the-money call.

instead of replacing the underlying position with a deeply in-the-money call, we can sell a deeply in-the-money put:

short a cal1 long a put short a deeply in-the-money put.

This type of position, where the underlying instrument in a conversion or reversal is replaced with a deeply in-the-money option, is known as a three-way .

Suppose we also execute a reversal at 90:

long a June 90 call short a June 90 put short an underlying contract.

short a June 100 call long a June 100 put long an underlying contract.

The long and short underlying contracts cancel out, leaving:

long a June 90 call short a June 90 put.

short a June 100 call long a June 100 put.

This position, known as a box, is similar to a conversion or reversal, except that any risk associated with holding a position in the underlyíng contract has been eliminated because the underlying position has been replaced with a synthetic underlying position at a different exercise price.

Since a box eliminates the risk associated with carrying a position in the underlying contract, boxes are even less risky than conversions and reversals, which are themselves low-risk strategies.

JELLY ROLLS.

Another method of eliminating a position in the underlying contract is to take a synthetic position in a different expiration month, rather than at a different exercise price as with a box.

For example, suppose we have executed the following reversal:

long a June 100 call short a June 100 put short an underlying contract.

short a September 100 call long a September 100 put long an underlyíng contract.

If the underlyíng contract for bothJune and Septernber is identical, theywil1 cancel out, leaving us with:

long a June 100 cal1 short a June 100 put.

short a September 100 cal1 long a September 100 put.

These combined long and short synthetic positions taken at the same exercise prices but in different expiration months is known as a jelly roll or simplya roll.

The value of the roll is the cost of holding the stock for the three-month period from June to September.

jelly roll = long-term synthetic - short-term synthetic = (long-term call-long-term put) - (short-term call-short-term put) = (long-term call-short-term call) - (long-term put - short-term put) = caηying costs - expected dividends.

USING SYNTHETICS IN VOLATILITY SPREADS.

the synthetic relationship:

synthetic short cal1 = short put + short underlying.

TRADING WITHOUT THEORETICAL VALUES.

Regardless of the exact theoretical value, there ought to be a uniform progression of both individual option prices and spread prices in the marketplace. If this uniform progression is violated, a trader can take advantage of the situation by purchasing the option or spread which is relatively cheap and selling the option or spread which is relatively expensive.

The trader can start with conversions and reversals, then look at vertical spreads and butterflies, and finally consider straddles and time spreads.

Early Exercise of American Options.

Given the opportunìty, under what cìrcumstances might a trader consìder exercising an American option prior to expiration? How much more should a trader be wi1ling to pay for an American option over an equivalent European option?

FUTURES OPTIONS.

option value = ìntrinsic value + volati1ìty value - interest rate value.

A trader who exercises a futures option early does so to capture the interest on the option's intrinsic value. This intrinsic value will be credited to his account only if the option is subject to stock-type settlement.

OPÇÕES DE AÇÕES.

Early Exercise of Calls for the Dividends.

call value = intrînsic value + interest rate value + volatility value - dividend value.

Since the only reason a trader would ever consider exercising a stock option call early is to receive the dividend, if a stock pays no dividend there is no reason to exercise a call early. If the stock does paya dividend, the only time a trader ought to consider early exercise is the day before the stock goes ex-dividend. At no other time in its life is a stock option call an early exercise candidate.

put value = intrinsic value - interest rate value + volatility value + dividend value.

Whereas a stock option call can only be an early exercise candidate on the day prior to the stock's ex-dividend date, a stock option put can become an early exercise candidate anytime the interest which can be earned through the sale of the stock at the exercise price is sufficiently large.

infer two conditions which are necessary before a trader considers exercising option early to capture is additional profit:

The option must be trading at parity. The option must have a delta close to 100.

The importance of early exercise is greatest when the underlying contract is a stock or physical commodity. In such a case there is a significant difference between the carrying cost on an option and the caπyi cost on underlying position. This difference will especially affect the difference between European and Am erican put values, since early exercise wil1 allow the trader to earn interest on the proceeds from the sale at the exercise price. An option trader in either the stock or physical commodity market will find that the additional accuracy offered by an American model, such as the Cox-Ross-Rubenstein or Whaley models, will indeed be worthwhile.

THE EFFECT OF EARLY EXERCISE ON TRADING STRATEGIES.

Cobertura com Opções.

PROTECTIVE CALLS AND PUTS.

The simplest wayωhedge an underlying position using optìons is to purchase either a call to protect a short position, or a put to protect a long position.

Since each strategy combines an underlying position with an option position, it follows from Chapter 11 that the resulting protected position is a synthetic option:

short underlying + long call = long put long underlying + long put = long call.

COVERED WRITES.

The value of typical covered writes, also known as overwrites, are covered call and covered put.

As with the purchase of a protective optlon, a covered write consists of a position in the under ng and an option. It can therefore be expressed as a synthetic position:

long underlying + short call = short put short underlying + short put =short call.

A popular strategy, known as a fence, is to simultaneously combine the purchase of a protective option with the sale ofa covered option. For example, with an underlying contract at 50, a hedger with a long position might choose to simultaneously sell a 55 call and purchase a 45 put.

Fences are popular hedging tools because they offer known protection at alow cost, or even a credit. At the same time ，they still allow a hedger to participate, at least partially, in favorable market movement. Fences go by a variety of names: range forwards, tunnels, cylinders; among floor traders they are sometimes known as split price conversions and reversals.

COMPLEX HEDGING STRATEGIES.

As a first step in choosing a strategy, a hedger might consider the following:

Does the hedge need to offer protection against a I'worst case" scenario? How much of the current directional risk should the hedge eliminate? What additional risks is the hedger willing to accept?

ll otnel ctors being equal, in a high implied volatility market a hedger should buy as few options as possible and sell as many options as possible. Conversely, in a low implied volatility market a hedger should buy as many options as possible and sell as few options as possible.

A hedger who constructs a position with unlimited risk in either direction is presumably taking a volatility position. There is nothing wrong with this, since volatility trading can be highly profitable. But a true hedger ought not lose sight of what his ultimate goal is: to protect an existing position, and to keep the cost of this protection as low as possible.

PORTFOLIO INSURANCE.

if he wants to replicate the combination of the underlying asset and the 100 put, he must sell off 43% of his holdings in the asset. When he does that, he will have a position theoretically equivalent to owning a 100 call.

This process ofcontinuously rehedging an underlying position to replicate an option position is often referred to as portfolio insurance.

If the mix of securities in a portfolio approximates an index, and futures contracts are available on that index, the manager can approximate the results of portfolio insurance by purchaslng or selling futures contracts to increase or decrease the holdings in his portfolio.

Even if options are available on an underlying asset, a hedger may still choose to effect a portfolio insurance strategy himself rather then purchasing the option in the marketplace. For one thing, he may consider the option too expensive. If he believes the option is theoretically overpriced, in the long run it will be cheaper to continuously rehedge the portfo1io. Or he may find insufficient luidity in the option market to absorb the number of option contracts he needs to hedge his position. Finally, the expiration of options which are available may not exactly correspond to the period over which he wants to protect his position. If an option is available, but expires earlier than desired, the hedger might still choose to purchase options in marketplace, and then pursue a portfolio insurance strategy over the period following the option's expiration.

Volatility Revisited.

SOME VOLATILITY CHARACTERISTICS.

we might surmise at an underlying contract is likely to have a typicallong-term average, or mean volatility. Moreover, the volatility of the underlying contract appears to be mean reverting. When volatility rises above the mean, one can be fairly certain that it will eventually fall back to its mean; when volatility fal1 s below the mean, one can be fairly certain that it will eventual1y rise to its mean.

VOLATILITY FORECASTING.

In addition ωthe mean reverting characteristic, volatility also tends to exhibit sen. al correlatton. The volatility over any given period is likely ωdepend on, or correlate with, the volatility over the previous period, assuming that both periods cover the same amount of time. If the volatilityofa contract over the last fourweeks was 15% , the volatility over the next four weeks is more likely to be close to 15% an far away from 15%.

A PRACTICAL APPROACH.

Rather than asking what the correct volati1ity is, a trader might instead aSk, given the current volatiUty climate, what' right strategy? Rather than trying to forecast an exact volatility, a trader will try to pick a strategy that best fits the volatility conditions in the marketplace. To do this, a trader will want to consider several factors:

What is long. term mean volatility of underlying contract? What has been the recent historical volatility in relation to em volatility? What is trend in recent historical volatility? Where îs imp1ied volatility and what is its trend? Are we dealing wi options of shorter or longer duration? How stable does the volati1ity tend to be?

SOME THOUGHTS ON IMPLIED VOLATILITY.

Implied versus Historical Volatility.

Market participants are making the logical assumption that what has happened in the past is a good indicator of what will happen in the future.

the fluctuations in implied volatility were usually less than the fluctuations in historical volatility. When the historical volatility declined, the implied volatility rarely dec1ined by an equal amount. And when historical volatility increased, the implied volatility rarely increased byan equal amount. Because volatility tends to be mean reverting, when historical volati1ity is above its mean there is a greater likelihood that it will dec1ine, and when historical volatility is below its mean there is a greater likelihood that it will increase.

Stock Index Futures and Options.

professional arbitrageurs find at in spite of the highly luid and usually efficient index markets, pricing disparities occur often enough to warrant close monitoring of these markets. When a disparity does exist, a trader can execute an arbitrage by hedging the mispriced index against either other stock indices or against a basket of stocks. Such arbitrage strategies are commonly refeηed to as index arbitrage .

CALCULATING AN INDEX.

There are several different methods of calculating stock index values, but the most common methods entail weighting the stocks either by price or by capitalization.

REPLICATING AN INDEX.

the number of shares of each stock required to replicate an index.

for a price weighted index: point value / index divisor.

for a capitalization weighted index: outstanding shares x point value / index divisor.

FUTUROS DO ÍNDICE DE AÇÕES.

The purchase of a futures contract offers one important advantage over the purchase of the component stocks: no cash outlay ís required to purchase a futures contract. Consequently, there is an interest rate savings equal to the cost of borrowing sufficient cash to purchase all the stocks in the index.

INDEX ARBITRAGE.

If the futures príce doesn't reflect the fair value, a trader can execute a profitable arbitrage by purchasing the undervalued asset, either the basket of stocks or the futures contract, and selling overvalued asset.

This type of trading strategy, where one buys or sells a mispriced stock index futures contract and takes an opposing position in the underlying stocks, is one type of index arbitrage. Since computers can often be programmed to calculate the fair value of a futures contract, and to execute the arbitrage when the futures contract is mispriced, such astrategy is also commonly referred to as program trading. A buy prograrn consists of buying the stocks and selling the futures contract, and a sell program consists of selling the stocks and buying the futures contract.

INDEX OPTIONS.

There are real1y two types of stock index options, those where the underlying is a stock index futures contract, and those where the underlying is the index itself.

Options on Stock Index Futures.

Although the ultirnate decision about the underlying price is trader's, in a stock index futures option rnarket a trader should be very careful about using an underlying futures price different from the quoted price. As we have already seen ，出 theoretical value of astock index futures contract depends information which rnay ot be readily available to the trader. If he 1s wrong about the price at which the index is actually trading because the individual stock prices do not reflect the true rnarket, his theoretical evaluation of the futures contract wil1 be incorrect.

It may seem odd, but in fact it doesn't matter whether the index opens the next morning at a higher price, lower price, or unchanged. What matters is that the marketplace believes that the market will change, and that all contracts are priced accordingly. In such a case, the trader rnust exercise those options which, given the perceived change in the underlying price, now have a value less than parity, and replace them with other contracts which are not limited by parity constraints.

Because it can be difficult to trade a complete and correctly proportioned basket of stocks, and because there is the additional risk of early exercise after an index arbitrage has been executed, mispriced synthetic relationships are not as easy to exploit ín index option markets as in other option markets.

Opção Volatilidade e Precificação: Estratégias e Técnicas Avançadas de Negociação: Estratégias e Técnicas Avançadas de Negociação.

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Descrição.

dado para aprender as estratégias de negociação e técnicas de gestão de risco necessárias para o sucesso nos mercados de opções.

em si, este texto permite novos e experientes.

comerciantes para aprofundar em muitos aspectos dos mercados de opções, incluindo:

maiores bolsas de derivativos e firmas comerciais.

compreensão mais completa de como os modelos teóricos de preços funcionam. E, o melhor de tudo, você aprenderá como aplicar os princípios da avaliação de opções para criar estratégias que, dada a avaliação de condições e tendências de mercado, tenham maiores chances de sucesso.

Opção Volatilidade e Preços: Advanced Trading Strategies and Technues, 2ª Edição.

Clique nas categorias de assunto deste livro para ver os títulos relacionados:

O QUE CADA OPERADOR DE OPÇÕES PRECISA SABER. O livro que todos os operadores devem ter.

O best-seller Opção Volatilidade e Preços fez Sheldon Natenberg uma autoridade amplamente reconhecida na indústria de opções. Em empresas em todo o mundo, o texto é muitas vezes o primeiro livro que novos comerciantes profissionais recebem para aprender as estratégias de negociação e técnicas de gerenciamento de risco necessárias para o sucesso nos mercados de opções.

Agora, nesta segunda edição revisada, atualizada e expandida, este profissional comercial de trinta anos apresenta o guia mais abrangente sobre estratégias e técnicas avançadas de negociação agora em impressão. Covering a wide range of topics as diverse and exciting as the market itself, this text enables both new and experienced traders to delve in detail into the many aspects of option markets, including: The foundations of option theory Dynamic hedging Volatility and directional trading strategies Risk analysis Position management Stock index futures and options Volatility contracts.

Clear, concise, and comprehensive, the second edition of Option Volatility & Pricing is sure to be an important addition to every option trader's library--as invaluable as Natenberg's acclaimed seminars at the world's largest derivatives exchanges and trading firms.

Você aprenderá como os operadores de opções profissionais se aproximam do mercado, incluindo as estratégias de negociação e técnicas de gerenciamento de risco necessárias para o sucesso. Você obterá uma compreensão mais completa de como os modelos de precificação teóricos funcionam. E, o melhor de tudo, você aprenderá a aplicar os princípios da avaliação de opções para criar estratégias que, dada a avaliação das condições e tendências do mercado, tenham maiores chances de sucesso.

A negociação de opções é uma ciência e uma arte. Este livro mostra como aplicar ambos ao efeito máximo.

Revisões do livro do cliente.

By David on Jan 11, 2015.

the bible of options trading.

By Felicia on Dec 30, 2014.

Great condition, item as expected.

By Kevin Rodrigue on Nov 12, 2014.

This is really all you need PERIOD. Well maybe Tastytrade. :)

A Must For Anyone Considering Trading Options.

By Apage on Feb 24, 2015.

This book is considered the "bible" on options implied volatility. Natenburg was a pioneer into this study decades ago, and his work is still relevant today. Anyone who is thinking about trading options should add this book to their library. This book covers everything from the Greeks, the Black-Scholes model, binomial options, to hedging with options, and much more . . . I recommend reading this book with pencil and graph paper in hand to work through some of the concepts to make sure you fully grasp what you are reading; the writing style is clear (if somewhat dry) and the author has no problem communicating his knowledge and fully teaching the reader the concepts, but this book builds on itself quickly and if you are unsure of some concept early on, and don't correct it, you will probably be lost in later sections. Although this book covers the fundamentals of options and normal distributions/standard deviations; it would greatly help knowing the fundamentals of the aforementioned concepts before reading this book to fully grasp the information presented.

By Paul M. Witt on Aug 04, 2015.

Top theoretical basis for options pricing and trading.

By Guangchao Zheng on Jun 18, 2015.

Buy the 1st Edition! The 2nd Edition is ruined with basic errors.

By Jon Smith on Apr 18, 2015.

In terms of content this book was outstanding. It provided great examples for a beginner learning options for the first time. I have taken a few option courses before and his strategies, technues and terminologies were helpful. They were a little on the beginner side but as a market risk professional I will not that against him as he described the book as the "first book that new professional traders are given to learn the trading strategies and risk management technues required for success in option markets." Given that it was outstanding. Now the reasons for the 1 rating: Simply put, the book is filled with basic 101 mistakes: 1) Simple mathematical errors such as multiplication versus addition occur throughout the book's example 2) It appears he overwrote examples (from the previous book?) with new numbers but he only partially updated the example at times. For instance: he will have 3 positions with a strike price of: 70, 75 & 80 and out of now where he ends up using 70, 75 & 65 for his three strikes. 3) He has several typos in which he states one thing twice and then the direct opposite a second later (usually the example is wrong). 4) The quantity of errors is surreal as makes you question the integrity of the book as a whole. 5) I would not say it is "advanced strategies and technues" but beginner to intermediate strategies and technues. While I found this book to be a good resource (since I placed the emphasis on the ideas and terms, not the examples), I would not recommend it as your first book (which he described it as). Based on the reviews of the 1st Edition, I would say buy that book as it may be the best book for options. If he spent the time and provided good examples, I would give this book 5 stars and say it was a must have for ever collection. But the errors occur too often and they break down at a basic level. For a basic book that is heavily flawed, I saw it should only be rated a 1. If I did not have prior experience in options (academic courses and professional experience), I would be confused. Fortunately, most of the mistakes that he makes are quite obvious and you should be able to correct them on your own even if you are learning it for your first time. Overall, I say buy the 1st edition and avoid this book like a plague. Overall, if he would have read the book over, he should have been able to easily catch his mistakes. It's a shame he did not take the time to review the book to make sure it was written correctly. I've very disappointed in Sheldon Natenberg as his first edition was consider the bible of options (still is). 2nd Edition was a complete failure.

By Drax on Sep 25, 2015.

Updated version has more detail and real world examples. Great intro to options.

By Igor Sushko on Nov 24, 2015.

Eu amo isso. Very deep and comprehensive book.

Most Important Book on Values in Options Trading.

By D. Gordon on Sep 11, 2015.

This is the book to read on the subject, because it is so well presented. Subtle details and consequences are explained in a very well written style that is easy to comprehend.

in depth about Volatility.

By Swampfish1 on Aug 22, 2015.

A thoughtful, detailed explanation of volatility and it's impact on pricing and probability. A serious read, requires study.

By Sammywig on Feb 29, 2016.

the industry standard for people new to option trading.

Strong on theory but weak on reality plus some careless errors.

By Chris G. Pflum on Nov 27, 2016.

This is the best book that I have read on the theoretical pricing model. It is well-written, the figures and tables reinforce the text, and the math is as simple as possible considering the complexity of the Black, Sholes, Merton model (model). Nevertheless, I have given the book only three stars because it does not confirm or compare its theoretical values with market data. Also, the book contains careless errors that should not exist after two editions. Although my comments concentrate on the book’s faults, I still strongly recommend it to serious traders who want to advance their understanding of options. The book fails to connect theory with reality. All the example trades, figures and tables are hypothetical. Option prices and the volatility that they imply (IV) are derived from the model. The book does not appear to use any market data. My specific comments point out discrepancies between the book’s hypothetical / theoretical findings and my observations of real market conditions. About a third of the book contains superfluous information that may not interest retail traders. This material includes lengthy discussions of arbitrage, market makers, synthetic conversions, and the effects of interest rates and dividends on option prices. I read and studied this material, but it has not influenced my trading. Page 228, Risk Considerations - Chapter 13 introduces and defines the concept of “theoretical edge” which is repeated throughout the book. The vague definition should be simplified and expressed in more concrete terms. It states, “theoretical edge – the average profit resulting from a strategy, assuming that the trader’s assessment of market conditions is correct.” Based on the data used to construct the spreads in this chapter, theoretical edge appears to be nothing more than the difference between an option’s theoretical and market price. Page 260, Using Synthetics in a Spreading Strategy - Instead of buying a long straddle: 1 June 100 call and 1 June 100 put, one could trade the synthetic equivalent: 2 June 100 calls and short 100 shares of the underlying stock. Here and elsewhere the text does not give practical advantages (e. g. risk vs reward) of using one versus the other. Pages 265 – 292, Option Arbitrage - Chapter 15 claims that “conversions and reversals are common strategies” (page 276), but towards the end of the chapter (page 288) Natenberg concedes that only an arbitrage trader who has low transaction costs and immediate access to the markets is likely to profit from conversions and reversals. Since the book seems inconsistent, I made simulated trades of conversions and reversals of the S&P 500 ETF (SPY) and held them until expiration. While risks were extremely low, the profits would not even cover the commissions. For example, on October 12, 2016 the SPY was trading at $213.82 and a 1 contract conversion would cost $21,396.00 (1 Oct 214 Put @ 1.82, -1 Oct 214 Call @ 1.68 and 100 SPY @ 213.82). At expiration, the conversion lost $2.50 ($2.50 profit - $5.00 commissions). Yields from other synthetic equivalents (boxes and rolls) were no better. While professional traders may profit from option arbitrage, retail traders who have limited funds and must pay commissions should avoid them. Pages 293 – 321, Early Exercise of American Options - According to Chapter 16, the decision to hold or exercise an option depends primarily on dividends and interest rates. The hypothetical trades assume that the stock pays a dividend before the option expires and interest rates are 6%. Presumably, if a stock does not pay a dividend and interest rates are near 0, none of this applies. The stock price is assumed to drop by the dividend amount on the same date that the dividend is paid. In practice, a stock’s price can drop on the X dividend date and then recover or drop further when the dividend is paid. I have personally seen this happen with Verizon (VZ) and AT&T (T). Unless the stock is paying a special, unscheduled dividend, I believe that the market will price the dividend into the stock making the adjustments described in this chapter unnecessary. Page 358, Maximum Gamma, Theta and Vega - Figure 18-10 illustrates that “Increasing the interest rate can cause the vega of a stock option to decline as time increases.” The vega values are plotted on three curves corresponding to interest rates that are assumed to stay fixed at 0%, 10% and 20% for up to 4 years. At first, vega increases for all the interest rates and after about 10 months vega declines but only if interest rates are at 20%. This figure, like others, makes extreme assumptions about interest rates just to illustrate a point. In the past 10 years, US interest rates have ranged from about 0% to 5.25%. Most of the theoretical examples in this book assume interest rate range from 6% to 20%. These rates are high even when compared to the 3% rate in 1994 when the first edition of this book was published. It seems odd that Natenberg devotes so much his book to the effects of interest rates, when they have very little effect on the short-term options that are actively traded. He admits as much towards the end of his book when he states, “Because most actively traded options tend to be short term, with expirations of less than one year, interest rates would have to change dramatically to have an impact on any but the most deeply in-the-money options.” (page 467, 3rd paragraph). Page 359, Binomial Option Pricing - The Cox – Ross – Rubinstein model was developed in the late 1970s as a “method of explaining basic option pricing theory to students without using advanced mathematics”. While this model (like the slide rule) may have been useful 40-50 years ago, it has no practical value today. Most trading platforms can instantly calculate an option’s theoretical value. Page 381, Volatility Revisited - Most of the figures in Chapter 20 illustrate that the implied volatilities (IV) trend from high to low going from short-term to long-term options (e. g., Figures 20-12, 20-13, 20-14, 20-18, 20-20 and 20-21). In contrast, I have observed that IV often runs in the opposite direction (i. e., short-term options have a lower IV than long-term options). Events such as earnings, acquisitions, mergers, stock buy-backs, elections and world events can trigger an IV surge at any expiration month that immediately follows the event. Implied volatility eventually reverts to a mean value, but it can stay below the mean for months and then suddenly jump above the mean and drop back in a few days. In my opinion, IV does not trend, but moves randomly above and below its moving average. Surprisingly, Natenberg does not discuss whether technical analyses could be applied to IV. To distinguish expensive options (with a high IV) from cheap ones (with a low IV), I use an “Implied Volatility Stochastic Oscillator” that plots the current implied volatility level as a percentage of its 52-week range. Page 412, Position Analysis - To simplify a complicated spread of puts, calls and the underlying stock, Natenberg converts the puts to their synthetic equivalents. For example, 19 March 65 puts are converted to 19 March 65 calls and short 1900 shares of the underlying stock. This type of conversion is valid only for puts and calls that have a delta of .50. The puts that are being converted, however, have different strikes and different deltas. Page 432, Some Thoughts on Market Making – The text assess the risks of a mixed collection of options that a market maker might accumulate over time; it states, “We will also assume that the implied volatility for June changes at 75 percent of the rate of change in April and the implied volatility for August changes at 50 percent of the rate of change in April.” Later on page 501 (1st paragraph) when discussing shifting the volatility, the text states, “… when the underlying price rises, implied volatility tends to fall; when the underlying price falls, implied volatility tends to rise.” In my opinion, the daily fluctuations in IV are random and frequently do not conform to projections that are based on a theoretical model. Although IV reverts to a mean, this reversion only becomes apparent in weekly or monthly charts. Over a period of days, IV stays mostly below its mean and makes brief surges above its mean. My point here is that IV is unpredictable over a 3 to 4 month time span. In my opinion, market data do not confirm these assumptions on IV rate of change and assertions that IV rises when the stock price falls or IV falls when the stock price rises. Chart 1 (attached to these comments) plots the daily price and IV of the Dow Jones Industrials (DIA) from March through October 2016. Note that price and IV do not correlate: • price trends up while IV does not trend; • price stays within one standard deviation of its linear regression while IV frequently moves more than one standard deviation above and below its linear regression; • price remains predominantly above its 120 day moving average while IV remains predominantly below its 120 day moving average. My point here is that other than distinguishing cheap from expensive options, the theoretical model does not project the month to month changes and trends in IV. Page 471, Volatility is Constant over the Life of the Option - Figures 23.3, 23.4 and 23.5 and the text state that at-the-money options decrease in value when volatility falls and increase in value when volatility rises. This relationship may be valid for the option’s theoretical value, but not for the market price. An option’s market price implies a volatility (IV) that does not correlate with the historical volatility (V) of the underlying asset. Chart 2 (attached to these comments) plots the daily IV and V of Eli Lily Corporation (LLY) from April to November 21, 2016. The upper chart shows that IV surged upward from August to November while V stayed range-bound. The lower chart shows that from May to November IV values were 1.2 X to 3 X higher than V. Since expensive options have a high IV, and cheap options have a low IV, these charts suggest that LLY options became increasingly expensive from May to November even though the volatility of the LLY stock stayed flat. Page 507, Implied Distributions – This section claims that an infinite number of butterfly spreads would have the same maximum value as just one spread. It states, “At expiration, the 95/100/105 butterfly (i. e. buy a 95 call, sell two 100 calls, buy a 105 call) will have a … maximum value of 5.00.” An infinite number of butterfly spreads at five point intervals would likewise “have a value of exactly 5.00.” Later (page 508) Natenberg invites the reader “to confirm that all the butterfly values do indeed sum to 5.00…”. Charts 3 and 4 (attached to these comments) plot butterfly spreads of the Nasdaq Index (QQQ) at 118.37. Chart 3 plots 2 butterfly spreads at .50 expiration intervals, and Chart 4 plots 4 butterfly spreads at the same expiration intervals. Using market values, my Tradestation platform calculated that the 2 butterfly spread would have a maximum value of $260.00 while the 4 butterfly spread would have a maximum value of $190.00. Perhaps if I had used the option’s theoretical values, as Natenberg presumably did, my butterflies would have confirmed “that all the butterfly values indeed sum to [the same value].” However, I think that Natenberg would have better served his readers if he had pointed out the significant difference between spreads constructed from options’ theoretical versus market values. Careless Errors Page 172, The text incorrectly shows that both a long and short strangle have a positive gamma, negative theta and positive vega. The short strangle should have negative gamma, positive theta and negative vega. Page 189, Figures 11-22 and 11.23, The figures incorrectly state that for both a long and short calendar spread the trader would buy a long term and sell a short term option. For the short calendar spread, the trader would sell the long term option and buy the short term option. Page 206, Figure 11-33, In short and long straddles the same number of puts and calls are sold or bought. Two of the six straddles in this figure sells more calls than puts, and one straddle buys more puts than calls. Page 260, 5th paragraph, The example of a bull put spread incorrectly buys and sells the same number of contracts of the same option. In other words, the spread does not exist. Page 329, 1st paragraph, The text states, “By comparing implied volatility with expected volatility over the life of the option, the hedger ought to be able to make a sensible determination as to whether he wants to buy or sell options.” What is “expected volatility”? The term is not defined in the glossary or appear in the index. Page 343, Figure 18.7, The number of occurrences used to calculate the average stock value should be 60 not 153. Page 359, Binomial Option Pricing, The 2nd paragraph states that one of the advantages of binomial option pricing is that you can assume “there are no interest or dividend considerations”. Interest and dividends are considered in the formulas and figures presented throughout this chapter. Page 412, The table in the middle of the page shows that 38 (19+19) March 65 puts were synthetically converted to 0 March 65 calls and 0 underlying stock. This is not possible. Page 447, 2nd paragraph, The price-weighted index value which was initially 100 should be 150. Pages 469 and 470, Figures 23-3 and 23-4. These figures supposedly illustrate how changes in price affect volatility; however, the axes are not labeled, and it’s not apparent what the charts are plotting. Page 471 last paragraph and Figure 23-5 – The text states, “When the price of the underlying remaining generally between 95 and 105, options with exercise prices of 95, 100, and 105 are worth more than the Black-Scholes value in a rising-volatility market and less than the Black-Sholes value in a falling-volatility market. “ All the option values in Figure 23-5 and perhaps the entire book were calculated from the Black-Sholes formula. In this case, it is not clear how option values that are calculated with the Black-Sholes formula could be “worth more than the Black-Sholes formula”. Page 502, Figure 24.14, The text in this figure should state: declining skew – not “investment” skew, and increasing skew – not “demand” skew. Chart 1, Dow Jones Industrial Average (DIA), Daily Price vs Implied Volatility Chart 2, Eli Lilly Corporation (LLY), Daily Implied Volatility (IV) vs Historic Volatility (Volatility Standard Deviation VSD) Chart 3, Nasdaq Index (QQQ), Maximum Profit of 2 Butterfly Spreads at .50 Expiration Intervals Chart 4, Nasdaq Index (QQQ), Maximum Profit of 4 Butterfly Spreads at .50 Expiration Intervals.

if you have an extensive math background you will find this book fairly easy. I have a degree in mathematics and knew .

By Matt Elgazar on Mar 03, 2015.

This book is for serious option traders. If you are just a guy at home that wants to learn a bit about options and don't have at least a bit of a math background then this book is not for you. However, if you have an extensive math background you will find this book fairly easy. I have a degree in mathematics and knew nothing about options before this book, so it was confusing at first. After learning the basics from other resources and resorting back to this i find that there is great information in here. I do not believe this book is completely out-dated. The pricing theories and spreading strategies are up to date and he clearly says (multiple times) that the average trader will have a hard time market making or creating arbitrage opportunities. That does not mean it's out-dated, it just means that you shouldn't try to trade like an arbitrage trader. Simples. BTW - for the one star comments that say they don't need to use Greeks to be successful trading options, you might as well just trade the underlying because option Greeks have so much to offer. If you are trading options without paying attention to Implied Volatility or the Greeks you are trading blind. If you are profitable this way then you're most likely making your money directionally, in which case you are much better off trading the underlying. You may have been very lucky if you are profitable trading options without paying attention to IV or Greeks. OR if you are very good at predicting the market direction then IV may have eaten way some of your profits. I highly recommend this book.

The Option Trading Bible.

By Steve Burns on Nov 09, 2013.

Over and over again the traders I respect most have recommended this book as the best option book to read for those interested in trading options. While I agree this is an excellent textbook for learning the complexities of option contracts along with most if not all of possible trading strategies. What I would consider is that this book reads basically like a school textbook and is a tough read, it took me quite awhile to get through it due to the denseness of the writing style. For new traders and those new to options I would suggest more basic books that are easier to start with and work your way up to this one as you progress in your understanding of option Greeks and how their prices are created. I would save this one as your fifth or sixth option book after you already have a handle on all the basics of options. This is one of the most informative and complete book on options just be ready to be able to understand it when you read it, this is not casual reading, it is for the serious option trader.

Opção Volatilidade & amp; Preços: Estratégias e Técnicas Avançadas de Negociação.

por Sheldon Natenberg.

Um dos livros mais lidos entre os operadores de opções ativas em todo o mundo, Option Volatility & amp; Pricing has been completely updated to reflect the most current developments and trends in option products and trading strategies.

Um dos livros mais lidos entre os operadores de opções ativas em todo o mundo, Option Volatility & amp; Pricing has been completely updated to reflect the most current developments and trends in option products and trading strategies.

Escrito de forma clara e fácil de entender, Option Volatility & amp; Preços aponta os principais conceitos essenciais para o sucesso comercial. Com base em sua experiência como trader profissional, o autor Sheldon Natenberg examina a teoria e a realidade da negociação de opções. Ele apresenta os fundamentos da teoria da opção, explicando como essa teoria pode ser usada para identificar e explorar oportunidades de negociação. Opção Volatilidade & amp; O preço ensina você a usar uma ampla variedade de estratégias de negociação e mostra como selecionar a estratégia que melhor se adapta à sua visão das condições de mercado e da tolerância a riscos individuais.

Opção Volatilidade & amp; Pricing, Advanced Trading Strategies and Technues.

Índice.

The language of options.

Especificações do contrato.

Call option: the right to buy or take a long position in a given asset at a fixed price on or before a specified data. Put option: the right to sell or take a short position in a given asset.

The difference between an option and a futures contract:

A futures contract requires delivery at a fixed price. The seller must make delivery and the buyer must take delivery of the asset. The buyer of an option can choose to take delivery(a call) or make delivery(a put).

The exercise price , or strike price is the price at which the underlying will be delivered should the holder of an option choose to exercise his right to buy or sell.

expiration date : The date after which the option may no longer be exercised is the expiration date.

The premium paid for an option can be separated into two components, the intrinsic value and the time value .

The additional amount ofpremium beyond the intrinsic value which traders are willing to pay for an option is the time value, sometimes also referred to as the option's time premium or extrinsic value.

An option's premium is always composed of precisely its intrinsic value and its time value. If a $400 gold call is trading at $50 with gold at $435 per ounce, the time value of the call must be $15 , since the intrinsic value is $35. Os dois componentes devem totalizar o prêmio total da opção de US $ 50.

If the option has no time value, its price will consist solely of intrinsic value. The option is trading at parity .

Any option which has a positive intrinsic value is said to be in-the-money by the amount of the intrinsic value. An option which has no intrinsic value is said to be out-of-the-money .

An option whose exercise price is identical to the current price of the underlying contract is said to be at-the-money , such an option is also out-of-the-money since it has no intrinsic value.

The distinction between an at-the-money and out-of-the-money option because an at-the-money option has the greatest amount of time premium and is usually traded very actively.

REQUISITOS DE MARGEM.

When a trader makes an opening trade on an exchange, the exchange may require the trader to deposit some amount of margin , or good faith capital.

Elementary Strategies.

SIMPLE BUY AND SELL STRATEGIES.

long and short an underlying contract.

long a call.

RISK REWARD CHARACTERISTICS.

long positions in 95, 100,and 105 calls.

the profit and loss from a short position in the 95, 100, and 105 calls.

long positions in 95, 100,and 105 puts.

the short put positions in 95, 100,and 105 puts.

COMBINATION STRATEGIES.

the profit and loss at expiration from the combined purchase of a 100 call for 2.70, and a 100 put for 3.70.

short them.

sell a 95 put for 1.55 and a 105 call for 1.15.

sell the 90 call and purchase the 100 call.

buy a 105 put for 7.10 and sell a 100 put for 3.70, for a total debit of 3.40.

CONSTRUCT AN EXPlRATION GRAPH.

If the graph bends, it wìll do so at an exercise price. Therefore, we can calculate the proflt or 10ss at each exercise price involved and simply connect these points with straight lines. If the position is 10ng and short equa1 numbers of cal1s (puts), the potential downside (upside) risk or reward wi11be equal ωthe total debit or credit required to establish the position. Ab ove highest exercise price all calls will go into-the-money, so the entire position will act like an underlying position which is either long or short underlying contracts equal to the number of net long or short calls. Below the lowest exercise price all puts will go into-the-money, so the entire position will act like an underlying position which is either long or short underlying contracts equal to the number of net long or short puts.

long one 95 call at 5.50 short three 105 calls at 1.15.

short one 90 cdll at 9.35 long two 100 calls at 2.70 short four 95 puts at 1.55 long two 100 puts at 3.70.

long one 100 call at 2.70 short one 100 put at 3.70.

long one 90 put at .45 short one 100 call at 2.70 long one underlying contract at 99.00.

Introduction to Theoretical Pricing Models.

If he purchases options, not only must he be right about market direction, he must also be right about market speed .

The minimum factors you must consider:

The price of the underlying contract. The exercise price. The amount of time remaining to expiration. The direction in which he expects the underlying market move. The speed at which he expects the underlying market to move.

THEORETICAL VALUE.

The two most common considerations in a financial investment are the expected return and carrying costs. And, in fact, dividends are an additional consideration in evaluating options on stock.

The goal of option evaluation is to determine, through the use of theoretical pricing models, the theoretical value of an option. The trader can then make an intelligent decision whether the option is overpriced or underpriced in the marketplace, and whether the theoretical edage is sufficient to justify going into the marketplace and making a trade.

A SIMPLE APPROACH.

We can now summarize the necessary steps in developing a model:

Propose a series of possible prices at expiration for the underlying contract. Assign an appropriate probability to each possible price. Maintain an arbitrage-free underlying market. From the prices and probabi1ities in steps 1, 2, and 3, calculate the expected return for the option. From the option's expected return, deduct the carrying cost.

In its original form, the Black-Scholes Model was intended to evaluate European options (no early exercise permitted) on non-dividend paying stocks. Shortly after its introduction, realizing that rnost stocks do pay dividends, Black and Scholes added a dividend cornponent. In 1976, Fischer Black rnade slight rnodifications to the rnodel to allow for the evaluation of options on futures contracts. And in 1983, Mark Garman and Steven Kohlhagen made several other modifications to allow for the evaluation of options on foreign currencies. The futures version and the foreign currencyversion are known officially as the Black Model and the Garman-Kohlhagen Model, respectively. But the evaluation rnethod in each version, whether the original Black-Scholes Model for stock options, the Black Model for futures options, or the Garman-Kohlhagen Model for foreign currency options, is so similar that they have all come to be known as simply the Black-Scholes Model. The various forrns of the model differ primarily in how they calculate the forward price of由eunderlying contract, and an option trader will simply choose the form appropriate to the underlying instrument.

In order to calculate an option's theoretical value using the Black-Scholes Model, we need to know at a minimum five characteristics of the option and its underlying contract. Tem:

The option's exercise price. The amount of time remaining to expiration. The current price of the underlying contract. The risk-free interest rate over the life of the option. The volatility of the underlying contract.

Black and Scholes also incorporated into their model the concept of the riskless hedge . To take advantage of a theoretically mispriced option，it is necessary to establish a hedge by offsetting the option position with this theoretically equivalent underlying position. That is, whatever option position we take, we must take an opposing market position in the underlying contract. The correct proportion of underlying contracts needed to establish this riskless hedge is known as the hedge ratlo .

Volatilidade.

RANDOM WALKS AND NORMAL DISTRIBUTIONS.

Thís leads to an important distínction between evaluation of an underlying contract and evaluation of an option. If we assume at prices are distributed along a normal distribution curve, the value of an underlying contract depends on where the peak of the curve is located, while the value of an option depends on how fast le curve spreads out.

LOGNORMAL DISTRIBUTIONS.

A continuously compounded rate of return of +12% yields a profit of $127.50 after one year, while a continuously compounded rate of return of -12% yields a loss of only $113.08.

When price changes are assumed to be normally distributed, the continuous compounding of these price changes wiU cause the prices at maturity to be lognormally distributed .

The Black-Scholes Model is a contínuous time model. It assumes at the volatility of an underlying instrument is constant over the life of the option, but that this volatility is continuously compounded. These two assumptions mean that the possible prices of the underlying instrument at expiration ofthe option are lognormally distributed.

It also explains why options with higher exercise prices caηy more value than options with lower exercise prices, where both exercise prices appear to be an identical amount away from the price of the underlying instrument.

Summarize the most irnportant assurnptions governing price movement int the Black-Scholes Model:

Changes in the price of an underlying instrurnent are randorn and cannot be artificially manipulated, nor is it possible to predict beforehand direction in which prices will move. The percent changes in the price of an underlying instrurnent are norrnally distributed. Because the percent changes in the price of the underlying instrurnent are assumed to be continuously cornpounded, the prices of the underlying instrument at expiration will be lognormally distributed. The mean of the lognormal distribution will be located at the forward price of the underlying contract.

TYPES OF VOLATILITIES.

Future Volatility: Future volatility is what every trader would like to know, the volatility at best describes the future distribution of prices for an underlying contract. Historical Volatility Forecast Volatility Implied Volatility: It is volatility being implied to the underlying contract through the pricing of the option in the marketplace. Even though the term premium real1y refers to an option's price, it is common among traders to refer to the implied volati1ity as the premium or premium level. If the current implied volatility is high by historical standards, or high relative to the recent historical volatility of the underlying contract, a trader might say that premium levels are high; if implied volatility is unusuallylow, he might say that premium levels are low.

He might then look at the difference between each option's theoretical value and its price in marke lace selling any options which were overpriced relative to the theoretical value, and buying any options which were underpriced.

Using an Option's Theoretical Value.

The purchase or sale of a theoretically mispriced option requires us to establish a hedge by taking an opposing positlon in the underlying contract. When this is done correctly, for small changes in the price of the underlying, the increase (decrease) in the value of the optlon position will exactly offset the decrease (increase) in the value of the opposing position in the underlying contract. Such a hedge is unbiased, or neutral , as to the direction of the underlying contract.

The number which enables us to establish a neutral hedge under current market conditions is a by-product of theoretical pricing model and is known as the hedge ratio or, more commonly, the delta .

The delta of a call option is always somewhere between 0 and 1.00. The delta of an option can change as market conditions change. An underlying contract always has a delta of 1.00.

The steps we have thus far taken illustrate the correct procedure in using an option theoretical value:

Purchase (sell) undervalued (overvalued) options. Establish a delta neutraI hedge against the underlying contract. Adjust the hedge at regular intervals to remain delta neutral.

At that time we plan to close out the position by:

Letting any out-of-the-money options expire worthless. Selling any in-the-money options at parity (intrinsic value) or, equiva1ently, exercising them and offsetting them against the underlying futures contract. Luidating any outstanding futures contracts at the market price.

1n a frictionless market we assume that:

Traders can freely buy or sell the underlying contract without restriction AlI traders can borrow and lend money at the same rate. Transaction costs are zero. There are no tax considerations.

Option Values and Changing Market Conditions.

three interpretations of delta:

the hedge ratio Rate of Change in the theoretical value: The de1ta is a measure of how an optio 's value changes with respect to a change in the price of the underlying contract. Theoretical or Equivalent Underlying Position.

The gamma sometimes referred to as the curvature of an option, is the rate at which an option's delta changes as the price of the underlying changes.

If an option has a gamrna of 5for each point rise (fal1) in the price of the und. erlying, the option will gain (lose) 5 de1tas.

Every option trader learns to look carefully not only at current directional risk (the delta), but also at how that directional risk will change if the underlying market begins ωmove (the gamma).

The theta(θ) ，or tíme decay factor, is the rate at which an option loses value as time passes.

THE VEGA OR KAPPA.

The vega of an option is usually given in point change ín theoretical value for each one percentage point change in volatility.

Since vega is not a Greek letter, a common alternative in academic literature, where Greek letters are preferred, is kappa (K).

A sensibilidade do valor teórico de uma opção a uma mudança nas taxas de juros é dada pelo seu rho (P).

Delta: Deltas range from zero for far out-of. the-money calls to 100 for deeply in-the-money calls, and from zero for far out-of-the-money puts to -100 for deeply in-the-money puts.

At-the-money calls have deltas of approximately 50, and at-the-money puts approximately -50.

As time passes, or as we decrease our volatility assumption, call deltas move away om 50,and puts deltas away from -50. As we increase our volatility assumption, cal1 deltas move towards 50, and put deltas towards -50.

As we increase our volati1ity assumptíon, the gamma of an in.

money option rises, while gamma of an at le.

money option falls. As we decrease our volatility assumption, or as time to expiration grows shorter, the gamma of an in.

the money option falls, while the gamma of an at.

the-money option rises, sometimes dramatically.

money options have greater etas than either in.

ofthe-money options with otherwise identical contract specifications.

The theta of an at-the-money option increases as expiration approaches. A short-term, at-the-money option will a1 ways decay more quickly than a long-term, at-the-money option.

As we increase (decrease) our volatility assumption, the theta of an option will rise (fall). Higher volatility means there is greater time value associated with the option, so at each day's decay wil1 also be greater when no movement occurs.

Out-of-the-money options have the greatest vega as apercent of theoretical value.

The various positions and their respective signs are given in Figure 6-26. The sign of the delta， gamma, theta, or vega, toge er with the magnitude of the numbers, tel1 the trader which changes in market conditions will either help or hurt his position, and to what degree. The positive or negative effect of changing market conditions is summarized in Figure 6-27.

An option's elasticity , sometimes denoted with the Greek letter omega(or less commonly the Greek letter lambda), is the relative percent change in an option's value for a given percent change in the price of the underlying contract.

The elasticity is sometimes referred to as the option's leverage value . The greater an option's elasticity, the more highly leverage the option.

An easy method of calculating:

elasticity = (underlying price) / (theoretical value) * delta.

Introduction to Spreading.

Spreading is simply a way of enabling an optlon trader to take advantage of theoretlcally mispriced options, while at the same time reducing the effects of short-term changes in market conditions so that he can safely hold an optlon positlon to maturity.

WHY SPREAD?

At some point the intelligent trader will have to consider not only the potential profit, but also the risk associated with a strategy.

No trader will survive very long if his livelihood depends on estimating each input with 100% accuracy. Even when he incorrectly estimates the inputs, the experienced trader can survive if he has constructed intelligent spread strategies which allow for a wide margin of error.

Volatility Spreads.

Regardless ofwhich method we choose, each spread will have certain features in common:

Eachspread will be approximately delta neutral. Cada spread será sensível a alterações no preço do instrumento subjacente. Each spread will be sensitive to changes in implied volatility. Each spread wil1 be sensitive to the passage of time.

BACKSPREAD.

A backspread is a delta neutral spread which consists of more long (purchased) options than short (sold) options where all options expire at the same time.

A call backspread consists of long calls at a higher exercise price and short calls at a lower exercise price. A put backspread consists of long puts at a lower exercise price and short puts at a higher exercise price.

If no movement occurs, a backspread is likely to be a losing strategy.

A trader will tend ωchoose the type ofbackspread which reflects his opinion about market direction. If he foresees a market with great upside potential, he will tend to choose a call backspread; if he foresees a market with great downside potential he will tend to choose a put backspread. He will avoid backspreads in quiet markets since the underlying contract is unlikely to move very far in either direction.

RATIO VERTICAL SPREAD.

A trader who takes the opposite side of a backspread also has a delta neutral spread, but he is short more contracts than long, with all options expiring at the same time. Such a spread is sometimes referred to as a ratio spread or a vertical spread.

Designe o oposto de um backspread como um spread vertical de proporção.

A straddle consists of either a long call and a long put, or a short call and a short put, where both options have the same exercise price and expire at the same time.

If both the call and put are purchased, the trader is said to be long the straddle; if both options are sold, the trader is said to be short the straddle.

Like a straddle, a strangle consists of a long call and a long put, or a short call and a short put, where both options expire at the same time. In a strangle, however， the options have different exercise prices. If both options are purchased, the trader is long the strangle if both options are sold, the trader is short the strangle.

To avoid confusion a strangle is commonly assumed to consist of out-the-money options. If the underlying market is current1y at 100 and a trader wants to purchase the June 95/105 strangle, it is assumed that he wants to purchase a June 95 put and a June 105 call. When both options are in-the-money, the position is sometimes referred to as a guts .

A butterfly consists of options at three equally spaced exercise prices, where all options are of the same type (either all calls or all puts) and expire at the same time.

In a long butterfly the outside exercise prices are purchased and the insíde exercise price is s01d, and vice versa for a short butterfly.

It is always 1 x 2 x 1, with two of each inside exercise price traded for each one of the outside exercíse prices. If the ratio is other than 1 x 2 x 1, the spread is no longer a butterfly.

a long butterfly tends to act like a ratio vertica1 spread and a short butterfly tends to act like a backspread.

TIME SPREAD (calendar spread or horizontal spread)

Time spreads, sometimes referred to as calendar spreads or horizontal spreads, consist of opposing positions whlch expire in different months. The most common type of time spread consists o.

The most common type of time spread consists of opposing positions in two options of the same type (either both calls or both puts) where both options have the same exercise price. When the long-term option is purchased and the short-term option is sold, a trader is long the time spread; when the short-term option is purchased and the long-term option is sold, the trader is short the time spread.

If we assume that the options making up a time spread are approxjmately at-the-money, time spreads have two important characteristics:

A long time spread always wants the underlying market sit still. Since a short-term at-the-money option always decays more quickly than a longterm at-the-money option, regardless of whether the options are calls or puts, both a long call time spread and a long put time spread want the underlying market to sit sti1l. Ideally, both spreads would like the short-term option to expire right at-the-money so that the long-term option will retain as much time value as possible while the short-term option expires worthless.

A long time spread always benefits jrom an increase in implied volatility. As time to expiration increases, the vega of an option increases. This means that a long-term option is always more sensitive in total points to a change in volatility than a short-term option with the same exercise price.

These two opposing forces, the decay in an option's value due to the passage of time and the change in an option's value due to changes in volatility, give time spreads their unue characteristics. When a trader buys or sel1s a time spread, he is not only attempting to forecast movement in the underlying market. He is剖sotrying to forecast changes in imp1ied volatility.

THE EFFECT OF CHANGING INTEREST RATES AND DIVIDENDS.

If we are considering stock options with different expiration dates, we mut consider two different forward prices. Andthese two forward prices may not be equaly sensitive to a change in interest rates.

If interest rates increase，the time spread will widen because the June forward price will rise more quickly than the March forward price. Therefore, a long (short) call time spread in the stock option market must have a positive (negative) rho.

if interest rates increase, the put time spread will narrow. Therefore, a long (short) put time spread in the stock option market must have a negative (positive) rho.

An increase (decrease) in dividends lowers (raises) the forward price of stock.

In a time spread, if a dividend payment is expected between expiration of the short-term and long-term option, the long-term option will be affected by the lowered forward price of the stock. Hence, an increase in dividends, if at least one dividend payment is expected between the expiration dates, will cause call time spreads to narrow and put time spreads to widen. A decrease in dividends will have the opposite effect, with call time spreads widening and put time spreads narrowing. The effect of changing interest rates and dividends on stock option time spreads is shown below:

DIAGONAL SPREADS.

A diagonal spread Is similar to a time spread, except that the options have different exercise prices.

OTHER VARIATIONS.

A Christmas tree (also referred to as a ladd is a term which can be applied to a variety of spreads. The spread usually consists of three different exercise prices where all options are of the same type and expire at the same time. In a long (short) call Christmas tree, one call is purchased (sold) at the lowest exercise price, and one call is sold (purchased) at each of the higher exercise prices. In a long (short) put Christmas tree, one put is purchased (sold) at the highest exercise price, and one put is sold (purchased) at each of the lower exercise prices.

Long Christmas trees , when done delta neutral， can be thought of as particular types of ratio vertical spreads. Such spreads therefore increase in value if the underlying market either sits still or moves very slowly. Short Christmas trees can be thought of as particular types of backspreads, and therefore increase in value with big moves in the underlying market.

It is possible to construct a spread which has the same characteristics as a butterfly by purchasing a straddle (strangle) and selling a strangle (straddle) where the straddle is executed at an exercise price midway between the strangle's exercise prices. All options must expire at the same time. Because the position wants the same outcome as a butterfly, it is known as an iron butterfly .

Another variation on a butterfly, known as a condor , can be constructed by splitting the inside exercise prices. Now the position consists of four options at consecutive exercise prices where the two outside options are purchased and the two inside options sold (a long condor), or the two inside options are purchased and the two outside options sold (a short condor). Como com uma borboleta, todas as opções devem ser do mesmo tipo (todas as chamadas ou todas as opções) e expirar ao mesmo tempo.

SPREAD SENSITIVITIES.

CHOOSING AN APPROPRlATE STRATEGY.

With so many spreads avai1 able, how do we know which type of spread is best?

Ideally, we would like ωconstruct a spread by purchasing options which are underpriced and se1li ng options which are overpriced.

If options general/y appear underprtced (low implied volatility), look for spreads with a positive vega. This includes strategies in backspread or long time spread category.!f options generally appear overpriced (high implied volatility)，look for spreads wtth a negative vega. This includes strategies in the ratio vertical or short time spread category.

Long time spreads are likely to be profitable when implied volatility is low but is expected to rise; short time spreads are likely to be profttable when implied volatility is high but is expected to fail.

ADJUSTMENTS.

O uso otimizado de um modelo teórico de precificação requer que um negociante mantenha continuamente uma posição neutra durante a vida útil do spread.

Adjust at regular intervals – In theory, the adjustment process is assumed to be continuous because volatility is assumed to be a continuous measure of the speed of the market. Adjust when the positlon becomes a predetermlned number 01 deltas or short. Adjust by feel.

ENTERING A SPREAD ORDER.

The following contingency orders, all ofwhich are defined in Appendix A, are often used in option markets:

Immediate Or Cancel.

Market If Touched.

Market On Close.

One Cancels The Other.

Stop Umit Order.

Ordem de Stop Loss.

Risk Considerations.

CHOOSING THE BEST SPREAD.

We can summarize these risks as follows:

Delta (DirectionaI) Risk-The risk that the underlying market will move in one direction rather than another. When we create a position which is delta neutral, we are trying to ensure that initially the position has no particular preference as to the direction in which the underlying instrument will move. A delta neutral position does not necessarily eliminate all directional risk, but it usually leaves us immune to directional risks within a limited range. Gamma (Curvature) Risk - The risk of a large move in the underlying contract, regardless of direction. The gamma position is a measure of how sensitive a position is to such large moves. A positive gamma position does not really have gamma risk since such a position will, in theory, increase in value with movement in the underlying contract. A negative gamma position, however, can quickly lose its theoretical edge with a large move in the underlying contract. The consequences of such a move must always be a consideration when analyzing the relative merits of different positions. Theta (Time Decay) Risk一Therisk that time will pass with no movement in the underlying contract. This is the opposite side of gamma risk. Positions with positive gamma become more valuable With large moves in the underlying. But if movement helps, the passage of time hurts. A positive gamma always goes hand in hand with a negative theta. A trader with a negative theta will always have to consider the risk in terms of how much time can pass before the spread's theoretical edge disappears. The position wants movement, but if the movement fails to occur within the next day, or next week, or next month, will be spread, in theory, still be profitable? Vega (Volatility) Risk — The risk that the volatility which we input into the theoretical pricing model will be incorrect. If we input an incorrect volatility, we will be assuming an incorrect distribution of underlying prices over time. Since some positions have a positive vega and are hurt by declining volatility, and some positions have a negative vega and are hurt by rising volatility, the vega represents a risk to every position. A trader must always consider how much the volatility can move againsthim before thepotential profit from a position disappears. Rho (Interest Rate) Risk-The risk that interest rates will change over the life of the option. A position with a positive rho will be helped (hurt) by an increase (decline) in interest rates, while a position with a negative rho wil1 show just the opposite characteristics. Generally, the interest rate is the least important of the inputs into a theoretical pricing model, and it is unlikely, except for special situations, that a trader will give extensive thought to rho risk associated with a position.

PRACTICAL CONSIDERATIONS.

While there is no substitute for experience, most traders quickly learn an important rule: straddles and strangles are the riskiest of all spreads.

HOW MUCH MARGIN FOR ERROR?

Perhaps a better way to approach the question is to ask not what is a reasonable margin for error, but rather to ask what is the correct size in which to do a spread given a known margin for error.

DIVIDENDS AND INTEREST.

WHAT IS A GOOD SPREAD?

It is impossible ωtake into consideration everypossible risk. A spread which passed every risk test would probably have so little theoretical edge that it wouldn't be worth doing. But the trader who allows himself a reasonable margin for error will find that even his losses will not lead to financial ruin. A good spread is not necessarily the one that shows the greatest proflt when things go well; it may be the one which shows the least loss when things go badly. Winning trades always take care of themselves. Losing trades, which don't glve back al1 the profits from the winning ones, are just as important.

ADJUSTMENTS.

An adjustment to trader's delta position may reduce his directional risk, but if he simultaneously increases his gamma, theta, or vega risk, he may inadvertently be exchanging one type of risk for another.

A delta adjustment made with the underlying contract is essentially a risk neutral adjustment. An adjustment made with options may reduce the delta risk, but will also change the other nsk characteristfcs assocíated wtth the position.

A disciplined trader knows that sometimes, because of risk considerations, the best course ls to reduce the size of the spread, even if it means gi. ving up some theoretical edge. This may be hard on the trader's ego, particular1y 1f he must personally go back into the market and either buy back options which he originally sold at a lower price, or sell out options whîch he originally purchased at a higher price. However, if a trader is unwilling to swallow his pride from time to time, and admit that he made a mistake, his trading career is certain to be a short one.

If a trader finds that any de1ta adjustment in the option market that reduces his risk will also reduce his theoretical edge，and he is unwil1ing to give up any theoretical edge, his only recourse is to make h1s adjustments in the underlying market. An underlying contract has no gamma, theta, or vega, so the risks of the position will remain essentially the same.

A QUESTION OF STYLE.

In practice, however, many option traders begin theîr trading careers by taking positions in the underlying market, where direction is the primary consideration. Many traders therefore deve10p a style of trading based on presumed directional moves in the underlying market. A trader might，for examp1e, be a trend follower, adhering to the philosophy that "the trend is your friend." Or he might be a contrarian. preferring to "buy weakness, sell strength."

An important consideration in deciding whether to enter into a trade is often the ease with which the trader can reverse the trade. Luid option markets, where there are many buyers and sellers, are much less risky than illuid markets, where there are few buyers and sellers. In the same way, a spread which consists of very luid options is much less risky出ana spread which consists of one or more illuid options.

Bull and Bear Spreads.

NAKED POSITIONS.

If all options are overpríced (high implied volatility), we might sell puts to create a bullish position, or sel1 calls to create a bearish position. If al1 options are underpriced (low implied volatility), we might buy calls ωcreate a bullish position, or buy puts to create a bearish position.

The problem with this approach is that，as with all non-hedged positions, there is very llttle margin error.

BULL AND BEAR RATIO SPREADS.

If a trader believes that implied volatility is too hlgh, one sensible strategy is a ratio vertical spread.

Even though the trader was correct ín his bullish sentiment, the position was primarily a volatility spread, so that the volatility characteristics of the position eventually outweighed any considerations of market direction.

Since this spread is a volatility spread, the primary consideration, as before, is the volatility of the market. Only secondarily are we concerned with the direction of movement. If the trader overestimates volatility, and the market moves more slowly than expected, the spread which was initially de1ta positive can instead become delta negative.

BULL AND BEAR BUTTERFLIES AND TlME SPREADS.

If the underlying market is currently at 100, he might choose to buy the June 105/110/115 call butterfly. Since this position wants the underlying market at 110 at expiration, and it is currently at 100, the position is a bull butterfly. This will be reflected in the position having a positive delta.

Unfortunately, if the underlying market moves too swift1y, say to 120, the butterfly can invert from a positive to a negative delta position.

Conversely, if the trader is bearish, he can always choose to buy a butterfly where the inside exercise price is below the current price of the underlying market. But again, if the market moves down too quickly and goes through the inside exercise price, the position will invert from a negative to a positive delta.

In a simi1ar manner, a trader can choose time spreads 由atare either bul1ish or bearish. A long time spread always wants the near-term contract to expire exactly at-the-money. A long time spread will be initial1y bullish if the exercise price of the time spread is above the current price of the underly1ng market.

SPREADS VERTICAIS.

Vertical spreads are not on1y initially bullish or bearish, but they remain bullish or bearish no matter how market conditions change. A vertical spread always consists of one long (purchased) option and one short (sold) option, where both options are of the same type (either both calls or both puts) and expire at the same time. The options are distinguished only by their different exercise prices. Typical vertical spreads might be:

buy 1 June 100 call.

sell 1 June 105 cal1.

buy 1 March 105 put.

sell 1 March 95 put.

If a trader wants to do a vertical spread, he has essentially four choices. If he is bullish he can choose a bull vertical call spread or a bull vertical put spread; if he is bearish he can choose a bear vertical call spread or a bear vertical put spread. Por exemplo:

bull call spread: buy a June 100 call.

bull put spread: buy a June 100 put.

bear call spread: sell a June 100 call.

bear put spread: sell a June 100 put.

Two factors determine the total directional characteristlcs of a vertlcal spread:

The delta of the specific vertical spread The size in which the spread is executed.

The greater the distance between exercise prices, the greater the delta value associated with the spread. A 95/110 bull spread wil1 be more bullish than a 100/110 bull spread, which will, ín turn, be more bullish than a 100/105 bull spread.

Once a trader decides on an expiratlon month in which to take his directlonal position, he must decide which specific spread is best. Ou seja, ele deve decidir quais preços de exercício usar. A common approach is focus on the at-the-money optlons. If a trader does this, he will have the fol1owing choices:

The reason becomes clear if we recall one of the characteristics of option evaluation introduced in Chapter 6: If we consider three options, an in-the-money， at-the-money， and out-of-the-money option which are identical except for their exercise prices, the at-the-money option is always the most sensitive in total points to a change in volatility.

This characteristic leads to a very simple rule for choosing bull and bear vertical spreads:

If implied volatility is too low, vertical spreads should focus on purchasing the at-the-money optlon. If implied volatility is too high, vertical spreads should focus on selling the at-the-money options.

A trader is not required to execute any vertical spread by first buying or selling the at-the-money option. Such spreads always involve two options, and a trader can choose to either execute the complete spread in one transaction, or leg into the spread by trading one option at a time. Regardless of how the spread is executed, the trader should focus on the at-the-money option, either buying it when implied volatility is too low, or selling it when implied volatility is too high.

The choice of the at-the-money option is slightly different when we move to stock options. If we define the at-the-money option as the one whose de1ta is closest to 50, then we may find at the at-the-money option is not always the one whose exercise price is closest current price of the underlying contract. This ís because the option with a delta closest 50 will be the one whose exercise price ís closest to forward price of underlying contract. In stock options, the forward price is the current price of stock, plus carrying costs on the stock, less expected dividends.

Why míght a trader with a directional opinion prefer a vertical spread to an outright long or short posítíon in the underlying instrument? For one thing, a vertical spread is much less risky than an outright posítion. Atrader who wants to take a position which is 500 deltas long can either buy fíve underlying contracts or buy 25 vertical calI spreads with a delta of 20 each. The 25 vertical spreads may sound riskier than five underlying contracts, until we remember at a vertical spread has limited risk whíle the position in underlying has open-ended risk. Of course, greater risk also means greater reward. A trader with a long or short position in the underlyíng market can reap huge rewards if the market makes a large move in his favor. By contrast, the vertical spreader's profits are limited, but he will also be much less bloodied if the market makes an unexpected move in the wrong direction.

Option Arbitrage.

SYNTHETIC POSITIONS.

synthetic long underlying = long call + short put synthetic short underlying = short call + long put.

where all options expire at the same time and have the same exercise price.

Rearranging the components of a synthetic underling position, we can create four other synthetic relationships:

synthetic long call = long an underlylng contract + long put synthetic short call = short an underlying contract + short put synthetic long put = short an underlying contract + long call synthetic short put = long an underlying contract + short call.

The difference between the call and put price ís often referred to as the synthettc market. In the absence of any interest or dividend considerations, the value of the synthetic market can be expressed as:

call price - put price = underlying price - exercise price.

If this equality holds, there ís no difference between taking a position in the underlying market, or taking an equivalent synthetic position in the option market.

The three-sided relationship between a call, a put, and its underlying contract means that we can always express the value of any one of these contracts in terms of the other two:

underlying price = call prîce - put prîce + exercíse price call prîce = underlying price + put príce - exercíse price put price = call prîce - underlying prîce + exercise price.

This three-sided relationship is sometimes referred put-call parity .

CONVERSIONS AND REVERSALS.

When a trader identifies two contracts which are essentially the same but which are trading at different prices, the natural course ís to execute an arbitrage by purchasing the cheaper contract and selling the more expensive.

No matter what happens in the underlying market, the underlying position will do exactly .25 better than the synthetìc position. The entire position wíll therefore show a profit of .25, regardless of movement in the underlying market.

The foregoing position, where the purchase of an underlying contract is offset by the sale of a synthetic position, is known as a conversion . The opposíte position, where the sale of an underlying contract is offset by the purchase of a synthetic position, is known as a reverse conversion or, more commonly, a reversal .

conversion = long underlying + synthetlc short underlying = long underlying + short call + long put reversal = short underlying + synthetic long underlying = short underlying + long call + short put.

As before, we assume that the call and the put have the same exercise price and expiration date.

Typically, an arbitrageur will attempt to simultaneously buy and sell the same items in different markets to take advantage of price discrepancies between the two markets.

Synthetic positions are often used to execute conversions and reversals, so traders sometimes refer to the synthetic market (the difference between the call price and put price) as the converston/reversal market.

All experienced traders are familiar with the price relationship between a synthetic position and its underlying contract, so that any imbalance in the conversion/reversal market is 1ikely to be short-lived. If the synthetic is overpriced, all traders will want to execute a conversion (buy the underlying, sell the call, buy the put). If the synthetic is underpriced, all traders will want to execute a reversal (sell the underlying, buy the call, sell the put). Such activity, where everyone is attempting to do the same thing, will quickly force the synthetic market back to equilibrium. De fato, os desequilíbrios no mercado de conversão / reversão são geralmente pequenos e raramente duram mais do que alguns segundos.

Futures Option Markets.

If the cash flow resulting from an option trade and a trade in the underlying instrument is identical, the synthetic relationship is simply:

call price - put price = underlying price - exercise price.

This will be true if interest rates are zero, or in futures markets where both the underlying contract and options on that contract are subject to futures-type settlement.

Assuming that all options are European (no early exercise permitted), we can now express the synthetic relationship in futures markets where the options are settle in cash as follows:

cal1 price - put price = futures price - exercise price - carrying costs.

where the carrying costs are calculated on either the difference between the futures price and the exercise price, or the difference between the call price and put price, both of which will be approximately the same.

Taking into consideration the interest rate component, we can express the synthetic relationship as:

call price - put price = stock price - exercise price + carrying costs.

where the carrying costs are calculated on the exercise price.

call price - put price = stock price - exercise price + carrying costs - dividends.

where the carrying costs are calculated on the exercise price and the dividends are those expected prior to expiration.

ARBITRAGE RISK.

Risco da taxa de juros.

Anytime a strategy is executed one leg at a time, there is always the risk of an adverse change in prices before the strategy can be completed.

The practical solution is to avoid carrying conversions and reversals to expiration when there is a real possibility of expiration right at the exercise price.

If al1 contracts are subject to futures-type settlement, any credit or debit resulting from changes in the price of the underlying futures contract wil1 be offset by an equal but opposite cash flow from changes in prices of the option contracts.

The risk arises because a synthetic position in options and an actual position in the underlying contract can have different characteristics， either in terms of settlement procedure, as in the futures option market, or in terms of the dividend payout, as in the stock option market.

How might we eliminate this risk?

short a call long a put long an underlying contract.

replace the long underlyingpositlon with a deeply in-the-money call Now our position is:

short a call long a put long a deeply in-the-money call.

instead of replacing the underlying position with a deeply in-the-money call, we can sell a deeply in-the-money put:

short a cal1 long a put short a deeply in-the-money put.

This type of position, where the underlying instrument in a conversion or reversal is replaced with a deeply in-the-money option, is known as a three-way .

Suppose we also execute a reversal at 90:

long a June 90 call short a June 90 put short an underlying contract.

short a June 100 call long a June 100 put long an underlying contract.

The long and short underlying contracts cancel out, leaving:

long a June 90 call short a June 90 put.

short a June 100 call long a June 100 put.

This position, known as a box, is similar to a conversion or reversal, except that any risk associated with holding a position in the underlyíng contract has been eliminated because the underlying position has been replaced with a synthetic underlying position at a different exercise price.

Since a box eliminates the risk associated with carrying a position in the underlying contract, boxes are even less risky than conversions and reversals, which are themselves low-risk strategies.

JELLY ROLLS.

Another method of eliminating a position in the underlying contract is to take a synthetic position in a different expiration month, rather than at a different exercise price as with a box.

For example, suppose we have executed the following reversal:

long a June 100 call short a June 100 put short an underlying contract.

short a September 100 call long a September 100 put long an underlyíng contract.

If the underlyíng contract for bothJune and Septernber is identical, theywil1 cancel out, leaving us with:

long a June 100 cal1 short a June 100 put.

short a September 100 cal1 long a September 100 put.

These combined long and short synthetic positions taken at the same exercise prices but in different expiration months is known as a jelly roll or simplya roll.

The value of the roll is the cost of holding the stock for the three-month period from June to September.

jelly roll = long-term synthetic - short-term synthetic = (long-term call-long-term put) - (short-term call-short-term put) = (long-term call-short-term call) - (long-term put - short-term put) = caηying costs - expected dividends.

USING SYNTHETICS IN VOLATILITY SPREADS.

the synthetic relationship:

synthetic short cal1 = short put + short underlying.

TRADING WITHOUT THEORETICAL VALUES.

Regardless of the exact theoretical value, there ought to be a uniform progression of both individual option prices and spread prices in the marketplace. If this uniform progression is violated, a trader can take advantage of the situation by purchasing the option or spread which is relatively cheap and selling the option or spread which is relatively expensive.

The trader can start with conversions and reversals, then look at vertical spreads and butterflies, and finally consider straddles and time spreads.

Early Exercise of American Options.

Given the opportunìty, under what cìrcumstances might a trader consìder exercising an American option prior to expiration? How much more should a trader be wi1ling to pay for an American option over an equivalent European option?

FUTURES OPTIONS.

option value = ìntrinsic value + volati1ìty value - interest rate value.

A trader who exercises a futures option early does so to capture the interest on the option's intrinsic value. This intrinsic value will be credited to his account only if the option is subject to stock-type settlement.

OPÇÕES DE AÇÕES.

Early Exercise of Calls for the Dividends.

call value = intrînsic value + interest rate value + volatility value - dividend value.

Since the only reason a trader would ever consider exercising a stock option call early is to receive the dividend, if a stock pays no dividend there is no reason to exercise a call early. If the stock does paya dividend, the only time a trader ought to consider early exercise is the day before the stock goes ex-dividend. At no other time in its life is a stock option call an early exercise candidate.

put value = intrinsic value - interest rate value + volatility value + dividend value.

Whereas a stock option call can only be an early exercise candidate on the day prior to the stock's ex-dividend date, a stock option put can become an early exercise candidate anytime the interest which can be earned through the sale of the stock at the exercise price is sufficiently large.

infer two conditions which are necessary before a trader considers exercising option early to capture is additional profit:

The option must be trading at parity. The option must have a delta close to 100.

The importance of early exercise is greatest when the underlying contract is a stock or physical commodity. In such a case there is a significant difference between the carrying cost on an option and the caπyi cost on underlying position. This difference will especially affect the difference between European and Am erican put values, since early exercise wil1 allow the trader to earn interest on the proceeds from the sale at the exercise price. An option trader in either the stock or physical commodity market will find that the additional accuracy offered by an American model, such as the Cox-Ross-Rubenstein or Whaley models, will indeed be worthwhile.

THE EFFECT OF EARLY EXERCISE ON TRADING STRATEGIES.

Cobertura com Opções.

PROTECTIVE CALLS AND PUTS.

The simplest wayωhedge an underlying position using optìons is to purchase either a call to protect a short position, or a put to protect a long position.

Since each strategy combines an underlying position with an option position, it follows from Chapter 11 that the resulting protected position is a synthetic option:

short underlying + long call = long put long underlying + long put = long call.

COVERED WRITES.

The value of typical covered writes, also known as overwrites, are covered call and covered put.

As with the purchase of a protective optlon, a covered write consists of a position in the under ng and an option. It can therefore be expressed as a synthetic position:

long underlying + short call = short put short underlying + short put =short call.

A popular strategy, known as a fence, is to simultaneously combine the purchase of a protective option with the sale ofa covered option. For example, with an underlying contract at 50, a hedger with a long position might choose to simultaneously sell a 55 call and purchase a 45 put.

Fences are popular hedging tools because they offer known protection at alow cost, or even a credit. At the same time ，they still allow a hedger to participate, at least partially, in favorable market movement. Fences go by a variety of names: range forwards, tunnels, cylinders; among floor traders they are sometimes known as split price conversions and reversals.

COMPLEX HEDGING STRATEGIES.

As a first step in choosing a strategy, a hedger might consider the following:

Does the hedge need to offer protection against a I'worst case" scenario? How much of the current directional risk should the hedge eliminate? What additional risks is the hedger willing to accept?

ll otnel ctors being equal, in a high implied volatility market a hedger should buy as few options as possible and sell as many options as possible. Conversely, in a low implied volatility market a hedger should buy as many options as possible and sell as few options as possible.

A hedger who constructs a position with unlimited risk in either direction is presumably taking a volatility position. There is nothing wrong with this, since volatility trading can be highly profitable. But a true hedger ought not lose sight of what his ultimate goal is: to protect an existing position, and to keep the cost of this protection as low as possible.

PORTFOLIO INSURANCE.

if he wants to replicate the combination of the underlying asset and the 100 put, he must sell off 43% of his holdings in the asset. When he does that, he will have a position theoretically equivalent to owning a 100 call.

This process ofcontinuously rehedging an underlying position to replicate an option position is often referred to as portfolio insurance.

If the mix of securities in a portfolio approximates an index, and futures contracts are available on that index, the manager can approximate the results of portfolio insurance by purchaslng or selling futures contracts to increase or decrease the holdings in his portfolio.

Even if options are available on an underlying asset, a hedger may still choose to effect a portfolio insurance strategy himself rather then purchasing the option in the marketplace. For one thing, he may consider the option too expensive. If he believes the option is theoretically overpriced, in the long run it will be cheaper to continuously rehedge the portfo1io. Or he may find insufficient luidity in the option market to absorb the number of option contracts he needs to hedge his position. Finally, the expiration of options which are available may not exactly correspond to the period over which he wants to protect his position. If an option is available, but expires earlier than desired, the hedger might still choose to purchase options in marketplace, and then pursue a portfolio insurance strategy over the period following the option's expiration.

Volatility Revisited.

SOME VOLATILITY CHARACTERISTICS.

we might surmise at an underlying contract is likely to have a typicallong-term average, or mean volatility. Moreover, the volatility of the underlying contract appears to be mean reverting. When volatility rises above the mean, one can be fairly certain that it will eventually fall back to its mean; when volatility fal1 s below the mean, one can be fairly certain that it will eventual1y rise to its mean.

VOLATILITY FORECASTING.

In addition ωthe mean reverting characteristic, volatility also tends to exhibit sen. al correlatton. The volatility over any given period is likely ωdepend on, or correlate with, the volatility over the previous period, assuming that both periods cover the same amount of time. If the volatilityofa contract over the last fourweeks was 15% , the volatility over the next four weeks is more likely to be close to 15% an far away from 15%.

A PRACTICAL APPROACH.

Rather than asking what the correct volati1ity is, a trader might instead aSk, given the current volatiUty climate, what' right strategy? Rather than trying to forecast an exact volatility, a trader will try to pick a strategy that best fits the volatility conditions in the marketplace. To do this, a trader will want to consider several factors:

What is long. term mean volatility of underlying contract? What has been the recent historical volatility in relation to em volatility? What is trend in recent historical volatility? Where îs imp1ied volatility and what is its trend? Are we dealing wi options of shorter or longer duration? How stable does the volati1ity tend to be?

SOME THOUGHTS ON IMPLIED VOLATILITY.

Implied versus Historical Volatility.

Market participants are making the logical assumption that what has happened in the past is a good indicator of what will happen in the future.

the fluctuations in implied volatility were usually less than the fluctuations in historical volatility. When the historical volatility declined, the implied volatility rarely dec1ined by an equal amount. And when historical volatility increased, the implied volatility rarely increased byan equal amount. Because volatility tends to be mean reverting, when historical volati1ity is above its mean there is a greater likelihood that it will dec1ine, and when historical volatility is below its mean there is a greater likelihood that it will increase.

Stock Index Futures and Options.

professional arbitrageurs find at in spite of the highly luid and usually efficient index markets, pricing disparities occur often enough to warrant close monitoring of these markets. When a disparity does exist, a trader can execute an arbitrage by hedging the mispriced index against either other stock indices or against a basket of stocks. Such arbitrage strategies are commonly refeηed to as index arbitrage .

CALCULATING AN INDEX.

There are several different methods of calculating stock index values, but the most common methods entail weighting the stocks either by price or by capitalization.

REPLICATING AN INDEX.

the number of shares of each stock required to replicate an index.

for a price weighted index: point value / index divisor.

for a capitalization weighted index: outstanding shares x point value / index divisor.

FUTUROS DO ÍNDICE DE AÇÕES.

The purchase of a futures contract offers one important advantage over the purchase of the component stocks: no cash outlay ís required to purchase a futures contract. Consequently, there is an interest rate savings equal to the cost of borrowing sufficient cash to purchase all the stocks in the index.

INDEX ARBITRAGE.

If the futures príce doesn't reflect the fair value, a trader can execute a profitable arbitrage by purchasing the undervalued asset, either the basket of stocks or the futures contract, and selling overvalued asset.

This type of trading strategy, where one buys or sells a mispriced stock index futures contract and takes an opposing position in the underlying stocks, is one type of index arbitrage. Since computers can often be programmed to calculate the fair value of a futures contract, and to execute the arbitrage when the futures contract is mispriced, such astrategy is also commonly referred to as program trading. A buy prograrn consists of buying the stocks and selling the futures contract, and a sell program consists of selling the stocks and buying the futures contract.

INDEX OPTIONS.

There are real1y two types of stock index options, those where the underlying is a stock index futures contract, and those where the underlying is the index itself.

Options on Stock Index Futures.

Although the ultirnate decision about the underlying price is trader's, in a stock index futures option rnarket a trader should be very careful about using an underlying futures price different from the quoted price. As we have already seen ，出 theoretical value of astock index futures contract depends information which rnay ot be readily available to the trader. If he 1s wrong about the price at which the index is actually trading because the individual stock prices do not reflect the true rnarket, his theoretical evaluation of the futures contract wil1 be incorrect.

It may seem odd, but in fact it doesn't matter whether the index opens the next morning at a higher price, lower price, or unchanged. What matters is that the marketplace believes that the market will change, and that all contracts are priced accordingly. In such a case, the trader rnust exercise those options which, given the perceived change in the underlying price, now have a value less than parity, and replace them with other contracts which are not limited by parity constraints.

Because it can be difficult to trade a complete and correctly proportioned basket of stocks, and because there is the additional risk of early exercise after an index arbitrage has been executed, mispriced synthetic relationships are not as easy to exploit ín index option markets as in other option markets.

Opção Volatilidade e Precificação: Estratégias e Técnicas Avançadas de Negociação: Estratégias e Técnicas Avançadas de Negociação.

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Descrição.

dado para aprender as estratégias de negociação e técnicas de gestão de risco necessárias para o sucesso nos mercados de opções.

em si, este texto permite novos e experientes.

comerciantes para aprofundar em muitos aspectos dos mercados de opções, incluindo:

maiores bolsas de derivativos e firmas comerciais.

compreensão mais completa de como os modelos teóricos de preços funcionam. E, o melhor de tudo, você aprenderá como aplicar os princípios da avaliação de opções para criar estratégias que, dada a avaliação de condições e tendências de mercado, tenham maiores chances de sucesso.

Opção Volatilidade e Preços: Advanced Trading Strategies and Technues, 2ª Edição.

Clique nas categorias de assunto deste livro para ver os títulos relacionados:

O QUE CADA OPERADOR DE OPÇÕES PRECISA SABER. O livro que todos os operadores devem ter.

O best-seller Opção Volatilidade e Preços fez Sheldon Natenberg uma autoridade amplamente reconhecida na indústria de opções. Em empresas em todo o mundo, o texto é muitas vezes o primeiro livro que novos comerciantes profissionais recebem para aprender as estratégias de negociação e técnicas de gerenciamento de risco necessárias para o sucesso nos mercados de opções.

Agora, nesta segunda edição revisada, atualizada e expandida, este profissional comercial de trinta anos apresenta o guia mais abrangente sobre estratégias e técnicas avançadas de negociação agora em impressão. Covering a wide range of topics as diverse and exciting as the market itself, this text enables both new and experienced traders to delve in detail into the many aspects of option markets, including: The foundations of option theory Dynamic hedging Volatility and directional trading strategies Risk analysis Position management Stock index futures and options Volatility contracts.

Clear, concise, and comprehensive, the second edition of Option Volatility & Pricing is sure to be an important addition to every option trader's library--as invaluable as Natenberg's acclaimed seminars at the world's largest derivatives exchanges and trading firms.

Você aprenderá como os operadores de opções profissionais se aproximam do mercado, incluindo as estratégias de negociação e técnicas de gerenciamento de risco necessárias para o sucesso. Você obterá uma compreensão mais completa de como os modelos de precificação teóricos funcionam. E, o melhor de tudo, você aprenderá a aplicar os princípios da avaliação de opções para criar estratégias que, dada a avaliação das condições e tendências do mercado, tenham maiores chances de sucesso.

A negociação de opções é uma ciência e uma arte. Este livro mostra como aplicar ambos ao efeito máximo.

Revisões do livro do cliente.

By David on Jan 11, 2015.

the bible of options trading.

By Felicia on Dec 30, 2014.

Great condition, item as expected.

By Kevin Rodrigue on Nov 12, 2014.

This is really all you need PERIOD. Well maybe Tastytrade. :)

A Must For Anyone Considering Trading Options.

By Apage on Feb 24, 2015.

This book is considered the "bible" on options implied volatility. Natenburg was a pioneer into this study decades ago, and his work is still relevant today. Anyone who is thinking about trading options should add this book to their library. This book covers everything from the Greeks, the Black-Scholes model, binomial options, to hedging with options, and much more . . . I recommend reading this book with pencil and graph paper in hand to work through some of the concepts to make sure you fully grasp what you are reading; the writing style is clear (if somewhat dry) and the author has no problem communicating his knowledge and fully teaching the reader the concepts, but this book builds on itself quickly and if you are unsure of some concept early on, and don't correct it, you will probably be lost in later sections. Although this book covers the fundamentals of options and normal distributions/standard deviations; it would greatly help knowing the fundamentals of the aforementioned concepts before reading this book to fully grasp the information presented.

By Paul M. Witt on Aug 04, 2015.

Top theoretical basis for options pricing and trading.

By Guangchao Zheng on Jun 18, 2015.

Buy the 1st Edition! The 2nd Edition is ruined with basic errors.

By Jon Smith on Apr 18, 2015.

In terms of content this book was outstanding. It provided great examples for a beginner learning options for the first time. I have taken a few option courses before and his strategies, technues and terminologies were helpful. They were a little on the beginner side but as a market risk professional I will not that against him as he described the book as the "first book that new professional traders are given to learn the trading strategies and risk management technues required for success in option markets." Given that it was outstanding. Now the reasons for the 1 rating: Simply put, the book is filled with basic 101 mistakes: 1) Simple mathematical errors such as multiplication versus addition occur throughout the book's example 2) It appears he overwrote examples (from the previous book?) with new numbers but he only partially updated the example at times. For instance: he will have 3 positions with a strike price of: 70, 75 & 80 and out of now where he ends up using 70, 75 & 65 for his three strikes. 3) He has several typos in which he states one thing twice and then the direct opposite a second later (usually the example is wrong). 4) The quantity of errors is surreal as makes you question the integrity of the book as a whole. 5) I would not say it is "advanced strategies and technues" but beginner to intermediate strategies and technues. While I found this book to be a good resource (since I placed the emphasis on the ideas and terms, not the examples), I would not recommend it as your first book (which he described it as). Based on the reviews of the 1st Edition, I would say buy that book as it may be the best book for options. If he spent the time and provided good examples, I would give this book 5 stars and say it was a must have for ever collection. But the errors occur too often and they break down at a basic level. For a basic book that is heavily flawed, I saw it should only be rated a 1. If I did not have prior experience in options (academic courses and professional experience), I would be confused. Fortunately, most of the mistakes that he makes are quite obvious and you should be able to correct them on your own even if you are learning it for your first time. Overall, I say buy the 1st edition and avoid this book like a plague. Overall, if he would have read the book over, he should have been able to easily catch his mistakes. It's a shame he did not take the time to review the book to make sure it was written correctly. I've very disappointed in Sheldon Natenberg as his first edition was consider the bible of options (still is). 2nd Edition was a complete failure.

By Drax on Sep 25, 2015.

Updated version has more detail and real world examples. Great intro to options.

By Igor Sushko on Nov 24, 2015.

Eu amo isso. Very deep and comprehensive book.

Most Important Book on Values in Options Trading.

By D. Gordon on Sep 11, 2015.

This is the book to read on the subject, because it is so well presented. Subtle details and consequences are explained in a very well written style that is easy to comprehend.

in depth about Volatility.

By Swampfish1 on Aug 22, 2015.

A thoughtful, detailed explanation of volatility and it's impact on pricing and probability. A serious read, requires study.

By Sammywig on Feb 29, 2016.

the industry standard for people new to option trading.

Strong on theory but weak on reality plus some careless errors.

By Chris G. Pflum on Nov 27, 2016.

This is the best book that I have read on the theoretical pricing model. It is well-written, the figures and tables reinforce the text, and the math is as simple as possible considering the complexity of the Black, Sholes, Merton model (model). Nevertheless, I have given the book only three stars because it does not confirm or compare its theoretical values with market data. Also, the book contains careless errors that should not exist after two editions. Although my comments concentrate on the book’s faults, I still strongly recommend it to serious traders who want to advance their understanding of options. The book fails to connect theory with reality. All the example trades, figures and tables are hypothetical. Option prices and the volatility that they imply (IV) are derived from the model. The book does not appear to use any market data. My specific comments point out discrepancies between the book’s hypothetical / theoretical findings and my observations of real market conditions. About a third of the book contains superfluous information that may not interest retail traders. This material includes lengthy discussions of arbitrage, market makers, synthetic conversions, and the effects of interest rates and dividends on option prices. I read and studied this material, but it has not influenced my trading. Page 228, Risk Considerations - Chapter 13 introduces and defines the concept of “theoretical edge” which is repeated throughout the book. The vague definition should be simplified and expressed in more concrete terms. It states, “theoretical edge – the average profit resulting from a strategy, assuming that the trader’s assessment of market conditions is correct.” Based on the data used to construct the spreads in this chapter, theoretical edge appears to be nothing more than the difference between an option’s theoretical and market price. Page 260, Using Synthetics in a Spreading Strategy - Instead of buying a long straddle: 1 June 100 call and 1 June 100 put, one could trade the synthetic equivalent: 2 June 100 calls and short 100 shares of the underlying stock. Here and elsewhere the text does not give practical advantages (e. g. risk vs reward) of using one versus the other. Pages 265 – 292, Option Arbitrage - Chapter 15 claims that “conversions and reversals are common strategies” (page 276), but towards the end of the chapter (page 288) Natenberg concedes that only an arbitrage trader who has low transaction costs and immediate access to the markets is likely to profit from conversions and reversals. Since the book seems inconsistent, I made simulated trades of conversions and reversals of the S&P 500 ETF (SPY) and held them until expiration. While risks were extremely low, the profits would not even cover the commissions. For example, on October 12, 2016 the SPY was trading at $213.82 and a 1 contract conversion would cost $21,396.00 (1 Oct 214 Put @ 1.82, -1 Oct 214 Call @ 1.68 and 100 SPY @ 213.82). At expiration, the conversion lost $2.50 ($2.50 profit - $5.00 commissions). Yields from other synthetic equivalents (boxes and rolls) were no better. While professional traders may profit from option arbitrage, retail traders who have limited funds and must pay commissions should avoid them. Pages 293 – 321, Early Exercise of American Options - According to Chapter 16, the decision to hold or exercise an option depends primarily on dividends and interest rates. The hypothetical trades assume that the stock pays a dividend before the option expires and interest rates are 6%. Presumably, if a stock does not pay a dividend and interest rates are near 0, none of this applies. The stock price is assumed to drop by the dividend amount on the same date that the dividend is paid. In practice, a stock’s price can drop on the X dividend date and then recover or drop further when the dividend is paid. I have personally seen this happen with Verizon (VZ) and AT&T (T). Unless the stock is paying a special, unscheduled dividend, I believe that the market will price the dividend into the stock making the adjustments described in this chapter unnecessary. Page 358, Maximum Gamma, Theta and Vega - Figure 18-10 illustrates that “Increasing the interest rate can cause the vega of a stock option to decline as time increases.” The vega values are plotted on three curves corresponding to interest rates that are assumed to stay fixed at 0%, 10% and 20% for up to 4 years. At first, vega increases for all the interest rates and after about 10 months vega declines but only if interest rates are at 20%. This figure, like others, makes extreme assumptions about interest rates just to illustrate a point. In the past 10 years, US interest rates have ranged from about 0% to 5.25%. Most of the theoretical examples in this book assume interest rate range from 6% to 20%. These rates are high even when compared to the 3% rate in 1994 when the first edition of this book was published. It seems odd that Natenberg devotes so much his book to the effects of interest rates, when they have very little effect on the short-term options that are actively traded. He admits as much towards the end of his book when he states, “Because most actively traded options tend to be short term, with expirations of less than one year, interest rates would have to change dramatically to have an impact on any but the most deeply in-the-money options.” (page 467, 3rd paragraph). Page 359, Binomial Option Pricing - The Cox – Ross – Rubinstein model was developed in the late 1970s as a “method of explaining basic option pricing theory to students without using advanced mathematics”. While this model (like the slide rule) may have been useful 40-50 years ago, it has no practical value today. Most trading platforms can instantly calculate an option’s theoretical value. Page 381, Volatility Revisited - Most of the figures in Chapter 20 illustrate that the implied volatilities (IV) trend from high to low going from short-term to long-term options (e. g., Figures 20-12, 20-13, 20-14, 20-18, 20-20 and 20-21). In contrast, I have observed that IV often runs in the opposite direction (i. e., short-term options have a lower IV than long-term options). Events such as earnings, acquisitions, mergers, stock buy-backs, elections and world events can trigger an IV surge at any expiration month that immediately follows the event. Implied volatility eventually reverts to a mean value, but it can stay below the mean for months and then suddenly jump above the mean and drop back in a few days. In my opinion, IV does not trend, but moves randomly above and below its moving average. Surprisingly, Natenberg does not discuss whether technical analyses could be applied to IV. To distinguish expensive options (with a high IV) from cheap ones (with a low IV), I use an “Implied Volatility Stochastic Oscillator” that plots the current implied volatility level as a percentage of its 52-week range. Page 412, Position Analysis - To simplify a complicated spread of puts, calls and the underlying stock, Natenberg converts the puts to their synthetic equivalents. For example, 19 March 65 puts are converted to 19 March 65 calls and short 1900 shares of the underlying stock. This type of conversion is valid only for puts and calls that have a delta of .50. The puts that are being converted, however, have different strikes and different deltas. Page 432, Some Thoughts on Market Making – The text assess the risks of a mixed collection of options that a market maker might accumulate over time; it states, “We will also assume that the implied volatility for June changes at 75 percent of the rate of change in April and the implied volatility for August changes at 50 percent of the rate of change in April.” Later on page 501 (1st paragraph) when discussing shifting the volatility, the text states, “… when the underlying price rises, implied volatility tends to fall; when the underlying price falls, implied volatility tends to rise.” In my opinion, the daily fluctuations in IV are random and frequently do not conform to projections that are based on a theoretical model. Although IV reverts to a mean, this reversion only becomes apparent in weekly or monthly charts. Over a period of days, IV stays mostly below its mean and makes brief surges above its mean. My point here is that IV is unpredictable over a 3 to 4 month time span. In my opinion, market data do not confirm these assumptions on IV rate of change and assertions that IV rises when the stock price falls or IV falls when the stock price rises. Chart 1 (attached to these comments) plots the daily price and IV of the Dow Jones Industrials (DIA) from March through October 2016. Note that price and IV do not correlate: • price trends up while IV does not trend; • price stays within one standard deviation of its linear regression while IV frequently moves more than one standard deviation above and below its linear regression; • price remains predominantly above its 120 day moving average while IV remains predominantly below its 120 day moving average. My point here is that other than distinguishing cheap from expensive options, the theoretical model does not project the month to month changes and trends in IV. Page 471, Volatility is Constant over the Life of the Option - Figures 23.3, 23.4 and 23.5 and the text state that at-the-money options decrease in value when volatility falls and increase in value when volatility rises. This relationship may be valid for the option’s theoretical value, but not for the market price. An option’s market price implies a volatility (IV) that does not correlate with the historical volatility (V) of the underlying asset. Chart 2 (attached to these comments) plots the daily IV and V of Eli Lily Corporation (LLY) from April to November 21, 2016. The upper chart shows that IV surged upward from August to November while V stayed range-bound. The lower chart shows that from May to November IV values were 1.2 X to 3 X higher than V. Since expensive options have a high IV, and cheap options have a low IV, these charts suggest that LLY options became increasingly expensive from May to November even though the volatility of the LLY stock stayed flat. Page 507, Implied Distributions – This section claims that an infinite number of butterfly spreads would have the same maximum value as just one spread. It states, “At expiration, the 95/100/105 butterfly (i. e. buy a 95 call, sell two 100 calls, buy a 105 call) will have a … maximum value of 5.00.” An infinite number of butterfly spreads at five point intervals would likewise “have a value of exactly 5.00.” Later (page 508) Natenberg invites the reader “to confirm that all the butterfly values do indeed sum to 5.00…”. Charts 3 and 4 (attached to these comments) plot butterfly spreads of the Nasdaq Index (QQQ) at 118.37. Chart 3 plots 2 butterfly spreads at .50 expiration intervals, and Chart 4 plots 4 butterfly spreads at the same expiration intervals. Using market values, my Tradestation platform calculated that the 2 butterfly spread would have a maximum value of $260.00 while the 4 butterfly spread would have a maximum value of $190.00. Perhaps if I had used the option’s theoretical values, as Natenberg presumably did, my butterflies would have confirmed “that all the butterfly values indeed sum to [the same value].” However, I think that Natenberg would have better served his readers if he had pointed out the significant difference between spreads constructed from options’ theoretical versus market values. Careless Errors Page 172, The text incorrectly shows that both a long and short strangle have a positive gamma, negative theta and positive vega. The short strangle should have negative gamma, positive theta and negative vega. Page 189, Figures 11-22 and 11.23, The figures incorrectly state that for both a long and short calendar spread the trader would buy a long term and sell a short term option. For the short calendar spread, the trader would sell the long term option and buy the short term option. Page 206, Figure 11-33, In short and long straddles the same number of puts and calls are sold or bought. Two of the six straddles in this figure sells more calls than puts, and one straddle buys more puts than calls. Page 260, 5th paragraph, The example of a bull put spread incorrectly buys and sells the same number of contracts of the same option. In other words, the spread does not exist. Page 329, 1st paragraph, The text states, “By comparing implied volatility with expected volatility over the life of the option, the hedger ought to be able to make a sensible determination as to whether he wants to buy or sell options.” What is “expected volatility”? The term is not defined in the glossary or appear in the index. Page 343, Figure 18.7, The number of occurrences used to calculate the average stock value should be 60 not 153. Page 359, Binomial Option Pricing, The 2nd paragraph states that one of the advantages of binomial option pricing is that you can assume “there are no interest or dividend considerations”. Interest and dividends are considered in the formulas and figures presented throughout this chapter. Page 412, The table in the middle of the page shows that 38 (19+19) March 65 puts were synthetically converted to 0 March 65 calls and 0 underlying stock. This is not possible. Page 447, 2nd paragraph, The price-weighted index value which was initially 100 should be 150. Pages 469 and 470, Figures 23-3 and 23-4. These figures supposedly illustrate how changes in price affect volatility; however, the axes are not labeled, and it’s not apparent what the charts are plotting. Page 471 last paragraph and Figure 23-5 – The text states, “When the price of the underlying remaining generally between 95 and 105, options with exercise prices of 95, 100, and 105 are worth more than the Black-Scholes value in a rising-volatility market and less than the Black-Sholes value in a falling-volatility market. “ All the option values in Figure 23-5 and perhaps the entire book were calculated from the Black-Sholes formula. In this case, it is not clear how option values that are calculated with the Black-Sholes formula could be “worth more than the Black-Sholes formula”. Page 502, Figure 24.14, The text in this figure should state: declining skew – not “investment” skew, and increasing skew – not “demand” skew. Chart 1, Dow Jones Industrial Average (DIA), Daily Price vs Implied Volatility Chart 2, Eli Lilly Corporation (LLY), Daily Implied Volatility (IV) vs Historic Volatility (Volatility Standard Deviation VSD) Chart 3, Nasdaq Index (QQQ), Maximum Profit of 2 Butterfly Spreads at .50 Expiration Intervals Chart 4, Nasdaq Index (QQQ), Maximum Profit of 4 Butterfly Spreads at .50 Expiration Intervals.

if you have an extensive math background you will find this book fairly easy. I have a degree in mathematics and knew .

By Matt Elgazar on Mar 03, 2015.

This book is for serious option traders. If you are just a guy at home that wants to learn a bit about options and don't have at least a bit of a math background then this book is not for you. However, if you have an extensive math background you will find this book fairly easy. I have a degree in mathematics and knew nothing about options before this book, so it was confusing at first. After learning the basics from other resources and resorting back to this i find that there is great information in here. I do not believe this book is completely out-dated. The pricing theories and spreading strategies are up to date and he clearly says (multiple times) that the average trader will have a hard time market making or creating arbitrage opportunities. That does not mean it's out-dated, it just means that you shouldn't try to trade like an arbitrage trader. Simples. BTW - for the one star comments that say they don't need to use Greeks to be successful trading options, you might as well just trade the underlying because option Greeks have so much to offer. If you are trading options without paying attention to Implied Volatility or the Greeks you are trading blind. If you are profitable this way then you're most likely making your money directionally, in which case you are much better off trading the underlying. You may have been very lucky if you are profitable trading options without paying attention to IV or Greeks. OR if you are very good at predicting the market direction then IV may have eaten way some of your profits. I highly recommend this book.

The Option Trading Bible.

By Steve Burns on Nov 09, 2013.

Over and over again the traders I respect most have recommended this book as the best option book to read for those interested in trading options. While I agree this is an excellent textbook for learning the complexities of option contracts along with most if not all of possible trading strategies. What I would consider is that this book reads basically like a school textbook and is a tough read, it took me quite awhile to get through it due to the denseness of the writing style. For new traders and those new to options I would suggest more basic books that are easier to start with and work your way up to this one as you progress in your understanding of option Greeks and how their prices are created. I would save this one as your fifth or sixth option book after you already have a handle on all the basics of options. This is one of the most informative and complete book on options just be ready to be able to understand it when you read it, this is not casual reading, it is for the serious option trader.

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Natenberg not only takes great pains to explain the concept of volatility, in addition to other inputs into an option pricing model, but clearly shows that option pricing isn't the exact science many seem to believe, for the simple reason that we never know if our volatility estimate is correct. I suspect many traders just don't understand the severe limitations current models have in different situations (ie. how the Black-Scholes model underprices options near expiration).

For the mathematically inclined, there are ample formulas and equations in the appendix.

Read it, study it, and apply the concepts to develop your own trading system.

If you're serious about trading I highly recommend reading this book first - it'll be a useful tool. Working at CBOE I have seen many other clerks studying their Natenberg books during the slower times. Learning arb (hand signaling) and understanding what you are arbing are the keys for a successful options trader. This can be useful for someone just getting started in options as well or with prior experience.