An Alternative Threshold GARCH Option Pricing Model: A Bayesian Approach

Abstract

This paper proposes an option pricing model, extended from the GARCH option pricing model of Duan (1995) and the Threshold-GARCH model of Hardle and Hafner (2000). Some moment properties of the proposed model are analytically proven. For simplicity or flexibility, the risk-free rate of return is treated as an estimate rather than a constant or a stochastic process. Parameter estimations are analyzed by the Bayesian approach via suitable MCMC techniques. Numerical illustrations are presented using some S&P 100 or 500 stock index series and call option price series. The posterior inference results indicate that the threshold effects on the volatility structure are significant. Moreover, the out-of-sample forecasting results also reveal that the inclusion of the threshold effect will indeed enhance the forecasting ability, especially, in the case of the out-of-the-money S&P 100 call option.