An empirical test of the variance gamma option pricing model

Abstract

In this paper, we test the 2-parameter symmetric variance gamma option pricing model and the 3-parameter asymmetric variance gamma option pricing model empirically. Prices of the Hang Seng Index call options which are of European style are used as the data for the empirical test. Since the VG option pricing model is developed for the pricing of European options, the empirical test gives a more conclusive answer than previous papers which used American option data to the applicability of the VG models. The present study uses a large number of intraday option data which span over a period of three years. Synchronous option and futures data are used throughout the study. Pairwise comparison between the accuracy of model prices are carried out using both parametric and non-parametric methods. When historical data are used to estimate model parameters based on which model prices are produced, the model pricing error is found to be much less for the VG models than for the Black-Scholes model. Between the symmetric VG and the asymmetric VG, the latter is found to have less error bias but have a larger standard deviation in error. Non-parametric test shows that the asymmetric VG fares better than the symmetric VG in option pricing. Thus, although the mean absolute error or mean squared error is less for SVG than for A VG, the reverse is true if some outlying A VG errors are discounted. As in Madan, Carr and Chang (1998) we show that the superior performance of the VG model is reflected in regression tests conducted on pricing errors. The results show that while the moneyness and maturity biases are prominent in the Black-Scholes model, the VG models, either symmetric or asymmetric, are relatively free of these errors. When model parameters are implied by a number of previously traded option prices, the model pricing error is also less for the VG models than for the Black-Scholes model, although the improvement is much less than is observed in the historical approach. The conclusion is that the VG models are useful models for option pricing and can produce model prices which approximate observed market prices better than the Black-Scholes approach.