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
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
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