Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money.
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| - Volatilitäts-Smile (de)
- Sorriso da volatilidade (pt)
- Volatility smile (en)
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| - Unter Volatilitäts-Smile (auch Volatilitätslächeln, englisch smile bedeutet ‚lächeln‘) wird in den Wirtschaftswissenschaften der Zusammenhang verstanden, dass die implizite Volatilität – dies ist jene, die nach dem Black-Scholes-Modell vorliegen muss, damit der aktuelle Marktpreis einer Option zustande kommt – umso niedriger ist, je mehr die Option „am Geld“ ist. Während das Phänomen des Volatilitäts-Smile bei Devisenoptionen schon länger zu beobachten war, trat es für Aktienoptionen erst nach dem Börsencrash von 1987 auf. (de)
- Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money. (en)
- Em Economia e Finanças, o sorriso da volatilidade é um padrão longo observado no qual opções dentro do dinheiro (ITM) tendem a ter menores do que as opções no dinheiro (ATM) ou fora do dinheiro (OTM). O padrão mostra características diferentes para diferentes mercados e resulta da probabilidade de movimentos extremos. Opções equity negociadas no mercado americano não mostraram um sorriso de volatilidade antes do mas o apresentaram posteriormente (pt)
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| - Unter Volatilitäts-Smile (auch Volatilitätslächeln, englisch smile bedeutet ‚lächeln‘) wird in den Wirtschaftswissenschaften der Zusammenhang verstanden, dass die implizite Volatilität – dies ist jene, die nach dem Black-Scholes-Modell vorliegen muss, damit der aktuelle Marktpreis einer Option zustande kommt – umso niedriger ist, je mehr die Option „am Geld“ ist. Häufig, insbesondere bei Devisenoptionen, steigt die implizite Volatilität sowohl bei Ausübungspreisen unterhalb als auch oberhalb des aktuellen Marktpreises an; sie hat also ihr Minimum bei Ausübungspreisen „am Geld“. Der Name des Begriffes kommt daher, dass die implizite Volatilität als Funktion in Abhängigkeit vom Ausübungspreis einen Kurvenverlauf ergibt, der an einen lächelnden Mund erinnert. Die Form der Volatilitätskurve ist abhängig vom jeweiligen Markt und vom Optionstyp. In vielen Fällen beobachtet man auch eine Schiefe (englisch skew), bei der die implizite Volatilität bei niedrigen Ausübungspreisen steigt und bei höheren Ausübungspreisen fällt. Während das Phänomen des Volatilitäts-Smile bei Devisenoptionen schon länger zu beobachten war, trat es für Aktienoptionen erst nach dem Börsencrash von 1987 auf. (de)
- Volatility smiles are implied volatility patterns that arise in pricing financial options. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. These options are said to be either deep in-the-money or out-of-the-money. Graphing implied volatilities against strike prices for a given expiry produces a skewed "smile" instead of the expected flat surface. The pattern differs across various markets. Equity options traded in American markets did not show a volatility smile before the Crash of 1987 but began showing one afterwards. It is believed that investor reassessments of the probabilities of fat-tail have led to higher prices for out-of-the-money options. This anomaly implies deficiencies in the standard Black–Scholes option pricing model which assumes constant volatility and log-normal distributions of underlying asset returns. Empirical asset returns distributions, however, tend to exhibit fat-tails (kurtosis) and skew. Modelling the volatility smile is an active area of research in quantitative finance, and better pricing models such as the stochastic volatility model partially address this issue. A related concept is that of term structure of volatility, which describes how (implied) volatility differs for related options with different maturities. An implied volatility surface is a 3-D plot that plots volatility smile and term structure of volatility in a consolidated three-dimensional surface for all options on a given underlying asset. (en)
- Em Economia e Finanças, o sorriso da volatilidade é um padrão longo observado no qual opções dentro do dinheiro (ITM) tendem a ter menores do que as opções no dinheiro (ATM) ou fora do dinheiro (OTM). O padrão mostra características diferentes para diferentes mercados e resulta da probabilidade de movimentos extremos. Opções equity negociadas no mercado americano não mostraram um sorriso de volatilidade antes do mas o apresentaram posteriormente A modelagem do "sorriso" da volatilidade é uma área ativa de pesquisa em finanças quantitativas. Tipicamente, um irá calcular a volatilidade implícita das "opções plain vanilla" e usa modelos de "sorriso" para calcular o preço de , que via de regra possuem termos mais complexos. Um conceito intimamente relacionado é o de estrutura a termo da volatilidade, que refere-se a como a volatilidade implícita difere para as opções relacionadas com diferentes maturidades. Uma superfície de volatilidade implícita é um gráfico 3-D que combina o sorriso da volatilidade e estrutura a termo da volatilidade em uma visão consolidada de todas as opções para um subjacente (pt)
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