This paper proposes an alternative Threshold-GARCH (TGARCH) option pricing model, which is a modification of the TGARCH model introduced by Härdle and Hafner (2000). Some moment properties of the proposed model are analytically proven. Parameter estimations are analyzed by the Bayesian approach via suitable Markov Chain Monte-Carlo (MCMC) techniques. Numerical illustrations are presented using a few S&P 100 and 500 stock index series and related 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 indeed enhances the forecasting ability, especially, in the case of the out-of-the-money S&P 100 call option.

Black and Scholes (1973) and Merton (1973) made a major breakthrough in stock option pricing. The importance of the model was recognized and it was successfully developed into an attractive research area in financial engineering. However, certain empirical anomalies challenge the Black-Scholes pricing formula. Considerable attention has been focused on the heteroskedasticity of the asset returns, e.g., the jump-diffusion model (Merton, 1976), and the bivariate diffusion model (Hull and White, 1987). The latest research results show that the degree of mispricing strongly depends on the volatility parameters and even more significantly on the correlation between the volatility and the stock price.

Since the Autoregressive Conditional Heteroskedasticity (ARCH) model was introduced by Engle (1982), it has been successfully applied to financial time series. The shape of the impact curve defined by Engle and Ng (1993) indicates that today’s volatility as a function of yesterday’s return is one of the dominating pricing factors. Duan (1995) pioneered a GARCH approach to option pricing, a discrete-time option pricing model for the case of a GARCH volatility process was proposed. In order to alleviate mispricing due to volatility misspecification, a flexible Threshold-GARCH (denoted by TGARCH hereafter) model was introduced by Härdle and Hafner (2000). Empirical results indicate that, for calls on the German stock index, DAX, the simulated TGARCH prices are closer to the market prices than either the Black-Scholes or the GARCH prices.

In this paper, an alternative TGARCH option pricing model has been proposed. Some analytical properties of the proposed model can be proven, including the first four moments of the error term and some correlations. Bayesian analysis techniques are applied for parameter estimation. From specified parameter prior distributions, posterior parameter distributions can be obtained by using a suitable Markov Chain Monte-Carlo (MCMC) sampling technique. In addition, the forecasting merits of the proposed model are investigated by applying few S&P call option prices.

Financial Risk Management Journal, Threshold-GARCH Option Pricing Model, Financial Engineering, Autoregressive Conditional Heteroskedasticity Model, Markov Chain Monte-Carlo Sampling Techniques, Bayesian Analysis, GARCH Model, Linear Regression Model, European Call Option, Black-Scholes Model, Bayesian Analysis Techniques, MCMC method.