Gaussian Stochastic Volatility Models: Scaling Regimes, Large Deviations, and Moment Explosions

Abstract

In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncorrelated Gaussian model grows faster than linearly, then, for the asset price process, all the moments of order greater than one are infinite. Similar moment explosion results are obtained for correlated models.

Keywords: Gaussian stochastic volatility models, Volterra type models, sample path large and moderate deviations, central limit regime, moment explosions, implied volatility asymptotics