Short-Maturity Asymptotics for a Fast Mean-Reverting Heston Stochastic Volatility Model

In this paper, we study the Heston stochastic volatility model in the regime where the maturity is small but large compared to the mean-reversion time of the stochastic volatility factor. We derive a large deviation principal and compute the rate function by a precise study of the moment generating function and its asymptotic. We then obtain asymptotic prices for Out-of-The-Money call and put options, and their corresponding implied volatilities.