We study fractional stochastic volatility models in which the volatility process is a positive continuous function \sigma of a continuous fractional stochastic process B. The main results obtained in the present paper are generalizations of large deviation principles for the log-price process due to Forde and Zhang. We assume that the function \sigma satisfies a relatively mild condition expressed in terms of its local modulus of continuity in L^2, while the process is a Volterra type Gaussian process. The assumptions used by Forde and Zhang are more restrictive. It is supposed in their work that the function \sigma satisfies a global H\"{o and the process B is fractional Brownian motion. We establish a small-noise large deviation principle for the log-price, and under \widehat{B}  an additional assumption of the self-similarity of the process \widehat{B}, derive a similar 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 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 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 . We assume that \sigma satisfies rather mild local regularity and growth conditions, while the process\widehat{B} is a Volterra type Gaussian process. Under an additional assumption of the self-similarity of the process \widehat{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.
D
fractional
R
The main results obtained in the present paper are generalizations of large deviation principles
Forde and Zhang established a large deviation principle
D
due to Forde and Zhang. We assume that the function \sigma satisfies a relatively mild condition expressed in terms of its local modulus of continuity in L^2, while the process
R
is a Volterra type Gaussian process. The assumptions used by Forde and Zhang are more restrictive. It is supposed in their work
in such a model under the assumptions
R
satisfies a global H\"{o
is globally H\"{o
R
We establish a
In the present paper, we prove a similar
R
for the log-price, and under
under weaker restrictions on \sigma and
A
. We assume that \sigma satisfies rather mild local regularity and growth conditions, while the process
A
is a Volterra type Gaussian process. Under
R
derive a similar
we derive a