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Implied Volatility in Stochastic Volatility Models

Peter Carr, Roger Lee

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Abstract

Abstract We survey how implied volatility relates to realized volatility, under general stochastic volatility dynamics. We consider implied volatility according to the Black–Scholes definition and also two model‐free definitions.

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Abstract We survey how implied volatility relates to realized volatility, under general stochastic volatility dynamics. We consider implied volatility according to the Black–Scholes definition and also two model‐free definitions.

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Available abstract

Abstract We survey how implied volatility relates to realized volatility, under general stochastic volatility dynamics. We consider implied volatility according to the Black–Scholes definition and also two model‐free definitions.

Key concepts: Stochastic volatility, Volatility (finance), Implied volatility, Forward volatility, Volatility smile, SABR volatility model, Volatility swap, Econometrics

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