Before revision:  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.
After revision:  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 models, and study the asymptotic behavior of call pricing functions and the implied volatility in mixed scaling regimes.