GARCH vs Stochastic Volatility: Option Pricing and Risk Management

This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. The models are calibrated to intraday FTSE 100 option prices. We apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk oriented measures. When we analyze the t to observed prices, GARCH clearly dominates both stochastic volatility and the benchmark Black Scholes model. However, the predictions of the market risk from hypothetical derivative positions show sizable errors. The t to the realized pro ts and losses is poor and there are no notable di erences between the models. Overall we therefore observe that the more complex option pricing models can improve on the Black Scholes methodology only for the purpose of pricing, but not for the Value-at-Risk forecasts.