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

2020/02/12 by Archil Gulisashvili, Gulisashvili, Archil
Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2002.05143

openalex publication_date 2020/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce time-inhomogeneous stochastic volatility models, in which the\nvolatility is described by a nonnegative function of a Volterra type continuous\nGaussian process that may have very rough sample paths. The main results\nobtained in the paper are sample path and small-noise large deviation\nprinciples for the log-price process in a time-inhomogeneous super rough\nGaussian model under very mild restrictions. We use these results to study the\nasymptotic behavior of binary barrier options, exit time probability functions,\nand call options.\n

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