Georgia Institute of Technology College of Sciences

It is commonly accepted that certain financial data exhibit long-range dependence. A continuous time stochastic volatility model is considered in which the stock price is geometric Brownian motion with volatility described by a fractional Ornstein-Uhlenbeck process. Two discrete time models are also studied: a discretization of the continuous model via an Euler scheme and a discrete model in which the returns are a zero mean iid sequence where the volatility is a fractional ARIMA process. A particle filtering algorithm is implemented to estimate the empirical distribution of the unobserved volatility, which we then use in the construction of a multinomial recombining tree for option pricing. We also discuss appropriate parameter estimation techniques for each model. For the long-memory parameter, we compute an implied value by calibrating the model with real data. We compare the performance of the three models using simulated data and we price options on the S&P 500 index. This is joint work with Prof. Alexandra Chronopoulou, which appeared in Quantitative Finance, vol 12, 2012.