Forecasting the Variability of Stock Index Returns with Stochastic Volatility Models and Implied Volatility

In this paper we compare the predictive abilility of Stochastic Volatility (SV) models to that of volatility forecasts implied by option prices. We develop an SV model with implied volatility as an exogeneous var able in the variance equation which facilitates the use of statistical tests for nested models; we refer to this model as the SVX model. The SVX model is then extended to a volatility model with persistence adjustment term and this we call the SVX+ model.<BR> This class of SV models can be estimated by quasi maximum likelihood methods but the main emphasis will be on methods for exact maximum likelihood using Monte Carlo importance sampling methods. The performance of the models is evaluated, both within sample and out-of-sample, for daily returns on the Standard & Poor's 100 index. Similar studies have been undertaken with GARCH models where findings were initially mixed but recent research has indicated that implied volatilityprovides superior forecasts. We find that implied volatility outperforms historical returns in-sample but that the latter contains incremental information in the form of stochastic shocks incorporated in the SVX models. The out-of-sample volatility forecasts are evaluated against daily squared returns and intradaily squared returns for forecasting horizons ranging from 1 to 10 days. For the daily squared returns we obtain mixed results, but when we use intradaily squared returns as a measure of realised volatility we find that the SVX+ model produces the most accurate out-of-sample volatility forecasts and that the model that only utilises implied volatility performes the worst as its volatility forecasts are upwardly biased. <BR><BR>