Large deviations for fractional volatility models with non-Gaussian volatility driver

We study non-Gaussian fractional stochastic volatility models. The volatility in such a model is described by a positive function of a stochastic process that is a fractional transform of the solution to an SDE satisfying the Yamada-Watanabe condition. Such models are generalizations of a fractional version of the Heston model considered in Bauerle and Desmettre (2020). We establish sample path and small-noise large deviation principles for the log-price process in a non-Gaussian model. We also illustrate how to compute the second order Taylor expansion of the rate function, in a simplified example. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

We study non-Gaussian fractional stochastic volatility models where the volatility is described by a fractional transform of the solution to an SDE satisfying the Yamada-Watanabe condition. These models are generalizations of a fractional version of the Heston model. We establish sample path and small-noise large deviation principles for the log-price process in a non-Gaussian model and illustrate how to compute the second order Taylor expansion of the rate function in a simplified example.