We study fractional stochastic volatility models in which the volatility process is a positive continuous function \sigma of a continuous stochastic process B. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function \sigma is globally H\"{o}lder-continuous and the process B is fractional Brownian motion. In the present paper, we prove a similar small-noise large deviation principle under weaker restrictions on \sigma and B. We assume that \sigma satisfies rather mild local regularity and growth conditions , while the process B is a Volterra type Gaussian process. Under an additional assumption of the self-similarity of the process B, we derive a large deviation principle in the small-time regime. As an application, we obtain asymptotic formulas for binary options, call and put pricing functions, and the implied volatility in certain mixed regimes.
We study fractional stochastic volatility models in which the volatility process is a positive continuous function \sigma of a continuous Gaussian process B. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function \sigma is globally H\"{o}lder-continuous and the process B is fractional Brownian motion. In the present paper, we prove a similar small-noise large deviation principle under weaker restrictions on \sigma and B. We assume that \sigma satisfies a mild local regularity condition , while the process B is a Volterra type Gaussian process. Under an additional assumption of the self-similarity of the process B, we derive a large deviation principle in the small-time regime. As an application, we obtain asymptotic formulas for binary options, call and put pricing functions, and the implied volatility in certain mixed regimes.
R
stochastic
Gaussian
R
rather
a
R
and growth conditions
condition