We study fractional stochastic volatility models for asset prices, 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 small-noise and small-time large deviation principles for the log-price process due to Forde and Zhang. It is assumed in the present paper that the function \sigma satisfies a relatively mild condition expressed in terms of its local modulus of continuity in L^2, while the process B 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 the global H\"{o}lder condition and the process B is fractional Brownian motion. In the present paper, we establish a small-noise large deviation principle for the log-price in a fractional stochastic volatility model , and under an additional assumption of the self-similarity of the process 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 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 B 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}lder condition and the process B is fractional Brownian motion. We establish a small-noise large deviation principle for the log-price , and under an additional assumption of the self-similarity of the process 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.
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for asset prices,
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small-noise and small-time
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the
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in a fractional stochastic volatility model