Small-time asymptotics for fast mean-reverting stochastic volatility models (Q453246)

The authors study stochastic volatility option-pricing models, where the maturity is small, but still large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging or homogenization problems for nonlinear HJB-type equations where the fast variable lives in a noncompact space.NEWLINENEWLINEThe authors develop a general argument based on viscosity solutions which they apply to the two regimes studied in the paper. They derive a large deviation principle and deduce asymptotic prices for out-of-the-money call and put options, and their corresponding implied volatilities.