Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices: Application of a Bivariate Kalman Filter
Dr Gael Martin, Department of Econometrics and Business Statistics, Monash University, Australia

Abstract:
In this paper we apply Bayesian methods to estimate a stochastic volatility model using both the prices of the asset and the prices of options written on the asset. Implicit posterior densities for the parameters of the volatility model, for the latent volatilities and for the market price of volatility risk are produced. The method involves augmenting the data generating process associated with a panel of option prices with the probability density function describing the dynamics of the underlying bivariate spot price and volatility process. Posterior results are produced via a hybrid Markov Chain Monte Carlo sampling algorithm. Candidate draws for the unobserved volatilities are obtained via the application of the Kalman filter and smoother to a linearization of the non-linear state-space representation of the model. Crucially, information from both the spot and option prices affects the draws via the specification of a bivariate measurement equation. The method is illustrated using the Heston (1993) stochastic volatility model, applied to spot and option price data on Australian News Corporation stock data. The way in which alternative option pricing models nested in the Heston framework can be ranked, via Bayes Factors and via fit, predictive and hedging performance, is also demonstrated.

(Joint work with Catherine Forbes and Jill Wright.)