Small-time asymptotics for fast mean-reverting stochastic volatility models
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.
Keywords
Cite
@article{arxiv.1009.2782,
title = {Small-time asymptotics for fast mean-reverting stochastic volatility models},
author = {Jin Feng and Jean-Pierre Fouque and Rohini Kumar},
journal= {arXiv preprint arXiv:1009.2782},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP801 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)