Asymptotic Implied Volatility at the Second Order with Application to the SABR Model
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Author | : Louis Paulot |
Publisher | : |
Total Pages | : 27 |
Release | : 2016 |
ISBN-10 | : OCLC:1306290920 |
ISBN-13 | : |
Rating | : 4/5 (20 Downloads) |
Book Synopsis Asymptotic Implied Volatility at the Second Order with Application to the SABR Model by : Louis Paulot
Book excerpt: 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.