Bayesian Forecasting of Options Prices: A Natural Framework for Pooling Historical and Implied Volatiltiy Information

Bayesian statistical methods are naturally oriented towards pooling in a rigorous way information from separate sources. It has been suggested that both historical and implied volatilities convey information about future volatility. However, typically in the literature implied and return volatility series are fed separately into models to provide rival forecasts of volatility or options prices. We develop a formal Bayesian framework where we can merge the backward looking information as represented in historical daily return data with the forward looking information as represented in implied volatilities of reported options prices. We apply our theory in forecasting the prices of FTSE 100 European Index options. We find that for forecasting options prices out of sample (i.e. one-day ahead) our Bayesian estimators outperform standard forecasts that use implied or historical volatilities. We find no evidence to suggest that standard procedures using implied volatility estimates are redundant in explaining market options prices.