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 anSV model with implied volatility as an exogeneous var able in the varianceequation which facilitates the use of statistical tests for nested models; werefer to this model as the SVX model. The SVX model is then extended to avolatility model with persistence adjustment term and this we call the SVX+model.This class of SV models can be estimated by quasi maximum likelihood methods butthe main emphasis will be on methods for exact maximum likelihood using MonteCarlo importance sampling methods. The performance of the models is evaluated,both within sample and out-of-sample, for daily returns on the Standard & Poor's100 index. Similar studies have been undertaken with GARCH models where findingswere initially mixed but recent research has indicated that impliedvolatilityprovides superior forecasts. We find that implied volatilityoutperforms historical returns in-sample but that the latter containsincremental information in the form of stochastic shocks incorporated in the SVXmodels. The out-of-sample volatility forecasts are evaluated against dailysquared returns and intradaily squared returns for forecasting horizons rangingfrom 1 to 10 days. For the daily squared returns we obtain mixed results, butwhen we use intradaily squared returns as a measure of realised volatility wefind that the SVX+ model produces the most accurate out-of-sample volatilityforecasts and that the model that only utilises implied volatility performes theworst as its volatility forecasts are upwardly biased.