Dr. Alexandra Chronopoulou (PSTAT, UCSB)

Title:Stochastic volatility models with long-memory in discrete and continuous time

Abstract: We consider a continuous time stochastic volatility model with long memory in which the stock price is described by a Geometric Brownian motion with volatility that follows a fractional Ornstein-Uhlenbeck process. In addition, we study two discrete time models: 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.

Using a particle filtering algorithm we estimate the empirical distribution of the unobserved volatility process for all three models. Based on the volatility filter, we construct 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.

Finally, we compare the different models using simulated data and we price options on the S&P 500 index.