Abstract

Bayesian statistical methods are naturally oriented towards pooling, in a rigorous way, information coming 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 (in- and out- of sample) the prices of FTSE 100 European index options. We find that for forecasting option prices out of sample (i.e. 1 day ahead), our Bayesian estimators outperform standard forecasts that use implied or historical volatilities particularly so when we assess the merit of the forecasts in economic or directional accuracy terms (i.e. in terms of the profit to a trading strategy).

7.1 Introduction

The purpose of this chapter is to propose a Bayesian approach for forecasting (in- and out- of sample) the prices of European options. In the classical Black Scholes (1973) framework and its subsequent extensions, this basically requires estimating ex ante the volatility of financial asset returns. As Engle and...