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We provide a short-time large deviation principle (LDP) for stochasticvolatility models, where the volatility is expressed as a function of aVolterra process. This LDP does not require strict self-similarity assumptionson the Volterra process. For this reason, we are able to apply such an LDP totwo notable examples of non self-similar rough volatility models: models wherethe volatility is given as a function of a log-modulated fractional Brownianmotion [Bayer et al., Log-modulated rough stochastic volatility models. SIAM J.Financ. Math, 2021, 12(3), 1257-1284], and models where it is given as afunction of a fractional Ornstein-Uhlenbeck (fOU) process [Gatheral et al.,Volatility is rough. Quant. Finance, 2018, 18(6), 933-949]. In both cases wederive consequences for short-maturity European option prices, impliedvolatility surfaces and implied volatility skew. In the fOU case we alsodiscuss moderate deviations pricing and simulation results.

Short-time asymptotics for non self-similar stochastic volatility models