Monte Carlo Methods for Derivative Pricing of Stochastic Volatility Models Driven by Fractional Brownian Motion

Abstract

We model asset prices with stochastic volatilities driven by fractional Brownian motion. Price paths and their endpoints are used to obtain a Monte Carlo value estimate of vanilla european options, lookback options as well as variance swaps. Underlying models for price movements are driven by stochastic volatility models driven by fractional Brownian motion with H > 1/2 . These models exhibit a strong autocorrelation in volatility evolution. The models considered are fractional Ornstein Uhlenbeck, fractional Cox-Ingersoll-Ross, fractional Continuous GARCH(1,1) and fractional Heston.