Multifactor volatility models: evidence from stock and option markets

Accumulating empirical evidence indicates that stock volatilities are driven by more than one latent factor. In this paper we provide additional evidence by combining FTSE100 stock-index data and three at-the-money option series of various maturities in a Kalman filter-based QML estimation strategy of multifactor affine stochastic volatility option pricing models (see Van der Ploeg et al. (2003)). We find that the volatility dynamics can satisfactorily be described by three independent volatility factors. In line with the literature, the first factor is extremely persistent. The second factor is much quicker mean-reverting. Shocks to this factor have a half-life of 2.5 months. The third factor is very fast mean-reverting, with shocks that have a half-life of about 10 days. We interpret the volatility factors in two ways. One interpretation is that each determines the long-term, middle-long-term and shortterm trends in the stock volatility evolution respectively. We show how each of the factors influences the prices of options of different maturities. Our second interpretation concerns their impact on the shape and dynamics of the volatility term structure. The long-memory factor appears mainly responsible for changes in the general level of the term structure. Slope changes are mainly associated with the second (but also the third) factor. Changes in the curvature of the volatility term structure are surprisingly closely related to the third factor.