Estimating the Parameters of Stochastic Volatility Models using Option Price Data

This paper describes a maximum likelihood method for estimating the parameters of Heston's model of stochastic volatility using data on an underlying market index and the prices of options written on that index. Parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options) are identified including the equity and volatility risk premia. The estimation is implemented using a particle filter. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using Graphical Processing Units. A byproduct of this focus on easing the computational burden is the development of a simplication of the closed-form approximation used to price European options in Heston's model. The efficacy of the filter is demonstrated under simulation and an empirical investigation of the fit of the model to the S&P 500 Index is undertaken. All the parameters of the model are reliably estimated and, in contrast to previous work, the volatility premium is well estimated and found to be significant.