Pricing and Headging with a Skewness and Kurtosis Adjusted Option Model in the Presence of Stochastic Volatility

It is well known that the volatility of asset returns is not constant, which has put forth the development of many option models incorporating a stochastic or GARCH process of volatility. Although these option models successfully reduce pricing and hedging errors of the Black-Scholes model, the complexity of the models often discourages market participants to utilize these models in pricing and hedging options. An alternative approach to adjust Black-Scholes model misspecification is to extend Black-Scholes model’s strict distributional assumption by adjusting non-lognormal skewness and kurtosis. This paper examines pricing and hedging performances of a skewness and kurtosis adjusted option model proposed by Jarrow and Rudd when volatility follows a stochastic process. Consistent with the previous research, the results of this study show that the skewness and kurtosis adjusted Jarrow-Rudd model reduces Black-Scholes pricing errors substantially especially for long-term, deep-in-the-money options. For hedging, however, improvements for the Jarrow-Rudd model over the Black-Scholes model are not virtually found. Overall, the study shows Jarrow-Rudd model could be a better alternative for the Black-Scholes model for option pricing but not necessarily for hedging. But considering the fact that Monte Carlo simulations employed in this study may subject to a model risk, the results of this simulation should be taken with caution.