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

Stefan Gerhold, Christoph Gerstenecker and Archil Gulisashvili

Stochastic Processes and their Applications, 2021, vol. 142, issue C, 580-600

Abstract: 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 Bäuerle 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.

Date: 2021
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DOI: 10.1016/j.spa.2021.09.010

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