Stochastic volatility : estimation and empirical validity
Estimation of stochastic volatility (SV) models is a formidable task because the presence of the latent variable makes the likelihood function difficult to construct. The model can be transformed to a linear state space with non-Gaussian disturbances. Durbin and Koopman (1997) have shown that the likelihood function of the general non-Gaussian state space model can be approximated arbitrarily accurately by decomposing it into a Gaussian part (constructed by the Kalman filter) and a remainder function (whose expectation is evaluated by simulation). This general methodology is specialised to the estimation of SV models. A finite sample simulation experiment illustrates that the resulting Monte Carlo likelihood estimator achieves full efficiency with minimal computational effort. Accurate values of the likelihood function allow inference within the model to be performed by means of likelihood ratio tests. This enables tests for the presence of a unit root in the volatility process to be constructed which are shown to be more powerful than the conventional unit root tests. The second part of the thesis consists of two empirical applications of the SV model. First, the informational content of implied volatility is examined. It is shown that the in- sample evolution of DEM/USD exchange rate volatility can be accurately captured by implied volatility of options. However, better forecasts of ex post volatility can be constructed from the basic SV model. This suggests that options implied volatility may not be market's best forecast of the future asset volatility, as is often assumed. Second, the regulatory claim of a destabilising effect of futures market trading on stock market volatility is critically assessed. It is shown how volume-volatility relationships can be accurately modelled in the SV framework. The variables which approximate the activity in the FT100 index futures market are found to have no influence on the volatility of the underlying stock market index.