Evidence on Delta Hedging and Implied Volatilities for the Black-Scholes, Gamma and Weibull Option-Pricing Models

Abstract

Modifying the distributional assumptions of the Black-Scholes model is one way to accommodate the skewness of underlying asset returns. Simple models based on the compensated gamma and Weibull distributions of asset prices have been shown to produce some improvements in option pricing. To evaluate these assertions, I construct and compare delta hedges of all S&P 500 options traded on the Chicago Board Options Exchange between September 2001 and October 2003 for the Weibull, the Black-Scholes, and the gamma models. I also compare implied volatilities and their smiles (i.e., non-linearities) among the three models. None of the three models improves over the others as far as delta hedging is concerned. Volatilities implied by all three models exhibit statistically significant smiles.