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 \omega-continuous for some modulus of continuity \omega. 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 optionsand binary call options.
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.
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extremely
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drift function and the volatility function are assumed to be time-dependent and locally \omega-continuous for some modulus of continuity \omega. The
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time-inhomogeneous super rough
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up-and-in barrier optionsand binary
barrier options, exit time probability functions, and