Gaussian stochastic volatility models: Scaling regimes, large deviations, and moment explosions

TL;DR

This paper investigates Gaussian stochastic volatility models, establishing large deviation principles and analyzing moment explosions, which are crucial for understanding rare events and tail risks in financial modeling.

Contribution

It provides the first comprehensive large deviation principles for Gaussian stochastic volatility models and characterizes moment explosions in uncorrelated and correlated cases.

Findings

Sample path large deviation principles established.

Moment explosions occur when volatility grows faster than linearly.

Asymptotic behaviors of exit probabilities and implied volatility analyzed.

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.