Time-Inhomogeneous Gaussian Stochastic Volatility Models: Large Deviations and Super Roughness

43 Pages Posted: 7 May 2020 Last revised: 31 Dec 2020

Date Written: April 12, 2020

Abstract

We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have extremely rough sample paths. The drift function and the volatility function are assumed to be time-dependent and locally ω-continuous for some modulus of continuity ω. The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a Gaussian model under very mild restrictions. We use these results to study the asymptotic behavior of binary up-and-in barrier options and binary call options.

Keywords: Gaussian stochastic volatility models, super rough models, sample path large deviation principle, logarithmic model, binary up-and-in barrier options, binary call options

JEL Classification: C02

Suggested Citation

Gulisashvili, Archil, Time-Inhomogeneous Gaussian Stochastic Volatility Models: Large Deviations and Super Roughness (April 12, 2020). Available at SSRN: https://ssrn.com/abstract=3574337 or http://dx.doi.org/10.2139/ssrn.3574337

Archil Gulisashvili (Contact Author)

Ohio University ( email )

Athens, OH 45701-2979
United States
740-593-1281 (Phone)
740-593-9805 (Fax)

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