Asymptotics for multifactor Volterra type stochastic volatility models

TL;DR

This paper extends the asymptotic analysis of stochastic volatility models to multidimensional Volterra processes, providing large deviation principles for scaled log-prices, even when the processes are not self-similar.

Contribution

It generalizes previous one-dimensional results to multidimensional Volterra models, establishing new large deviation principles for these complex stochastic volatility models.

Findings

Established pathwise large deviation principles for scaled log-prices.

Derived finite-dimensional large deviation principles for the models.

Extended asymptotic results to non-self-similar Volterra processes.

Abstract

We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper are a generalization of the results due, in the one-dimensional case, to Cellupica and Pacchiarotti [M. Cellupica and B. Pacchiarotti (2021) Pathwise Asymptotics for Volterra Type Stochastic Volatility Models. Journal of Theoretical Probability, 34(2):682--727]. We state some (pathwise and finite-dimensional) large deviation principles for the scaled log-price and as a consequence some (pathwise and finite-dimensional) short-time large deviation principles.