Abstract
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 noncompact 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 Feng, Forde and Fouque [SIAM J. Financial Math. 1 (2010) 126–141] by a moment generating function computation in the particular case of the Heston model.
Citation
Jin Feng. Jean-Pierre Fouque. Rohini Kumar. "Small-time asymptotics for fast mean-reverting stochastic volatility models." Ann. Appl. Probab. 22 (4) 1541 - 1575, August 2012. https://doi.org/10.1214/11-AAP801
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