We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a positive 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 result obtained in the paper is a sample path large deviation principle for the log-price process in a Gaussian model under very mild restrictions. We apply this result to study the first exit time of the log-price process from an open interval .
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 options and binary call options .
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is a sample path large deviation principle
are sample path and small-noise large deviation principles
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apply this result
use these results
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first exit time of the log-price process from an open interval
asymptotic behavior of binary up-and-in barrier options and binary call options