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Asymptotic Implied Volatility at the Second Order with Application to the SABR Model

Large Deviations and Asymptotic Methods in Finance, Springer (2015) 37-69

27 Pages Posted: 4 Jun 2009 Last revised: 18 May 2016

Date Written: June 3, 2009

Abstract

We provide a general method to compute a Taylor expansion in time of implied volatility for stochastic volatility models, using a heat kernel expansion. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatility, which we also give exactly at all strikes. As an application, we compute this asymptotic expansion at order 2 for the SABR model.

Keywords: stochastic volatility, asymptotic expansion, heat kernel, SABR

Suggested Citation

Paulot, Louis, Asymptotic Implied Volatility at the Second Order with Application to the SABR Model (June 3, 2009). Large Deviations and Asymptotic Methods in Finance, Springer (2015) 37-69. Available at SSRN: https://ssrn.com/abstract=1413649 or http://dx.doi.org/10.2139/ssrn.1413649

Louis Paulot (Contact Author)

Misys ( email )

42 rue Washington
Paris, 75008
France

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