Large deviation principle for Volterra type fractional stochastic volatility models

2017/10/29 by Gulisashvili, Archil
#FOS: Economics and business #Mathematical Finance (q-fin.MF)

paper · doi:10.48550/arxiv.1710.10711

Abstract

We study fractional stochastic volatility models in which the volatility process is a positive continuous function σ of a continuous Gaussian process \widehatB. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function σ is globally Hölder-continuous and the process \widehatB is fractional Brownian motion. In the present paper, we prove a similar small-noise large deviation principle under weaker restrictions on σ and \widehatB. We assume that σ satisfies a mild local regularity condition, while the process \widehatB is a Volterra type Gaussian process. Under an additional assumption of the self-similarity of the process \widehatB, 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.

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