A state space approach to the estimation of multi-factor affine stochastic volatility option pricing models

We propose a class of stochastic volatility (SV) option pricing models that is more flexible than the more conventional models in different ways. We assume the conditional variance of the stock returns to be driven by an affine function of an arbitrary number of latent factors, which follow mean-reverting Markov diffusions. This set-up, for which we got the inspiration from the literature on the term structure of interest rates, allows us to empirically investigate if volatilities are driven by more than one factor. We derive a call pricing formula for this class. Next, we propose a method to estimate the parameters of such models based on the Kalman filter and smoother, exploiting both the time series and cross-section information inherent in the options and the underlying simultaneously. We argue that this method may be considered an attractive alternative to the efficient method of moments (EMM). We use data on the FTSE100 index to illustrate the method. We provide promising estimation results for a 1-factor model in which the factor follows an Ornstein-Uhlenbeck process. The results indicate that the method seems to work well. Diagnostic checks show evidence of there being more than one factor that drives the volatility, indicate the existence of level-dependent volatility, and provide an incentive to consider realized volatility in future empirical analysis.