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Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models

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  • Matthew Lorig
  • Stefano Pagliarani
  • Andrea Pascucci

Abstract

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, $3/2$ stochastic volatility, and SABR local-stochastic volatility.
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  • Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    • Handle: RePEc:bla:mathfi:v:27:y:2017:i:3:p:926-960
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    File URL: http://hdl.handle.net/10.1111/mafi.2017.27.issue-3
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    References listed on IDEAS

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