Small-time asymptotics for fast mean-reverting stochastic volatility models

Details Small-time asymptotics for fast mean-reverting stochastic volatility models Small-time asymptotics for fast mean-reverting stochastic volatility models

2010-09-14

arxiv.org/abs/1009.2782v1

Economy

Quantitative Finance

Pricing of Securities

36 pages

Scientific paper

In this paper, we study stochastic volatility models in regimes where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB type equations where the "fast variable" lives in a non-compact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle and we deduce asymptotic prices for Out-of-The-Money call and put options, and their corresponding implied volatilities. The results of this paper generalize the ones obtained in \cite{FFF} (J. Feng, M. Forde and J.-P. Fouque, {\it Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model}, SIAM Journal on Financial Mathematics, Vol. 1, 2010) by a moment generating function computation in the particular case of the Heston model.

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