Fractional Stochastic Volatility Models and Applications in Pricing

Abstract.

The Black-Scholes model is one of the most important approaches to pricing options.One of the basic assumptions of this model is that volatility is constant, while in the real world volatility depends on the expiration time and strike price of the option.Therefore, in this thesis, we first introduce the Local volatility models and Stochastic volatility models, which consider the assumption of volatility Variability. And then we study the fractional stochastic volatility models in which the volatility is driven by a fractional Brownian motion and the price is driven by an independent simple Brownian motion. We relate the option price to a exponential average of the exponential fractional Brownian motion and we derive the asymptotics of the mentioned average as t tends to infinity