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

Archil Gulisashvili

Stochastic Processes and their Applications, 2021, vol. 139, issue C, 37-79

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 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.

Keywords: Gaussian stochastic volatility models; Super rough models; Sample path large deviation principle; Logarithmic model; Binary barrier options; Call options (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2021.04.012

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