Time-inhomogeneous Gaussian stochastic volatility models: Large deviations and super roughness

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 very rough sample paths. The main results obtained in the paper are sample path and small-noise large deviation principles for the log-price process in a time-inhomogeneous super rough Gaussian model under very mild restrictions. We use these results to study the asymptotic behavior of binary barrier options, exit time probability functions, and call options. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces time-inhomogeneous stochastic volatility models and obtains sample path and small-noise large deviation principles for the log-price process in a time-inhomogeneous super rough Gaussian model. These results are then used to study the asymptotic behavior of binary barrier options, exit time probability functions, and call options.