A 'Horse Race' Among Competing Option Pricing Models Using S&P 500 Index Options

Abstract

The last three decades have witnessed a whole array of option pricing models. We compare the predictive performances of a selection of models by carrying out a horse race on S&P 500 index options along the lines of Jackwerth and Rubinstein (2001). The models we consider include: Black-Scholes, trader rules, Heston's stochastic volatility model, Merton's jump diffusion models with and without stochastic volatility, and more recent Levy type models. Trader rules still dominate mathematically more sophisticated models, and the performance of the trader rules is further improved by incorporating the stable index skew pattern documented in Li and Pearson (2005). Furthermore, after incorporating the stable index skew pattern, the Black-Scholes model beats all mathematically more sophisticated models in almost all cases. Mathematically more sophisticated models vary in their overall performance and their relative accuracy in forecasting future volatility levels and future volatility skew shapes.

Keywords: option pricing models, performance comparison, implied skew

JEL Classification: G12, G13