In this paper, we study Gaussian stochastic volatility models. The evolution of volatility in such a model is described by a stochastic process, which can be represented as a nonnegative continuous function of a continuous Gaussian process. If the volatility process exhibits fractional features, then the model is called a Gaussian fractional stochastic volatility model. Important examples of fractional volatility processes are fractional Brownian motion, the Riemann-Liouville fractional Brownian motion, and the fractional Ornstein-Uhlenbeck process. If the volatility process admits a Volterra type representation, then the model is of Volterra type. In the paper, we provide a unified approach to various scaling regimes associated with Gaussian models. More precisely, large deviation, moderate deviation, and central limit scalings are introduced in the paper. We prove a sample path large deviation principle for the log-price process in a Volterra type Gaussian stochastic volatility model and a sample path moderate deviation principle for the same process in a Gaussian stochastic volatility model. We also study the asymptotic behavior of  call pricing functions  and the implied volatility in mixed scaling regimes. It is also shown that tail estimates arising in the large deviation theory are locally uniform. Another problem addressed in the paper concerns moment explosions for the asset price process in a Gaussian stochastic volatility model. We prove that for the asset price process in an uncorrelated Gaussian stochastic volatility model with the volatility function growing faster than linearly,  all the moments of order greater than one are infinite. Explosions of all the moments of order \gamma>(1-\rho^2)^{-1, where \rho is the correlation coefficient, are shown for correlated models, and partial }  results are obtained for the case where \gamma=(1-\rho^2)^{-1 .
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions , and the implied volatility . In addition, we prove that if the volatility function in an uncorrelated Gaussian model grows faster than linearly, then, for the asset price process, all the moments of order greater than one are infinite. , where \rho is the correlation coefficient, are shown for correlated models, and partial } Similar moment explosion results are obtained for correlated models .
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study Gaussian stochastic volatility models. The evolution of volatility in such a model is described by a stochastic process, which can be represented as a nonnegative continuous function of a continuous Gaussian process. If the volatility process exhibits fractional features, then the model is called a Gaussian fractional stochastic volatility model. Important examples of fractional volatility processes are fractional Brownian motion, the Riemann-Liouville fractional Brownian motion, and the fractional Ornstein-Uhlenbeck process. If the volatility process admits a Volterra type representation, then the model is of Volterra type. In the paper, we provide a unified approach to various scaling regimes associated with Gaussian models. More precisely, large deviation, moderate deviation, and central limit scalings are introduced in the paper. We prove a
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