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

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