Empirical Comparison of alternative option pricing models

Abstract

The unsatisfactory performance by the Black and Scholes model has led to a search for better alternatives that extend the classic model in one, or a combination, of three directions. In this study we make a choice among alternative option pricing models, made perhaps based on goodness of fit, forecasting and hedging effectiveness. To reach this goal, we choose three representative types of models that show a significant improvement over the Black and Scholes model. First model to be tested is the jump diffusion model. We study whether the jump component is really important for pricing and hedging short-term options through comparing the jump diffusion model with the stochastic volatility model and the stochastic volatility jump model from three perspectives: (1) internal consistency of implied parameters with relevant time series data, (2) out-of-sample pricing, and (3) hedging effectiveness. The stochastic volatility jump model shows the best performance for one day and one week out-of-sample pricing effectiveness, closely followed by the stochastic volatility model. The jump diffusion model exhibits the worst performance, and the differences between the performance of the stochastic volatility and the stochastic volatility jump models are not much. With these results, it is found that the jump component has only the marginal effect and the stochastic volatility term is of the most importance even for short-term options. However, it is hard to tell which one is the best model for hedging performance in the absolute sense. Second one is the stochastic volatility model. The stochastic volatility term provides a first-order improvement over the Black and Scholes (1973) model. We compare empirical performances of four classes of stochastic volatility option pricing models: (1) the ad hoc Black and Scholes procedure that fits the implied volatility surface, (2) Heston and Nandi ``s (2000) GARCH type model, (3) Madan, Carr, and Chang``s (1998) variance gamma model, ...