Economy – Quantitative Finance – Pricing of Securities
Scientific paper
2009-06-03
Economy
Quantitative Finance
Pricing of Securities
27 pages; v2: typos fixed and a few notation changes
Scientific paper
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.
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