Pricing Taiwan option market with GARCH and stochastic volatility

This study compares the out-of-sample performances among Black-Scholes (B-S), Stochastic Volatility (SV) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models in the Taiwan option market. Using Absolute Relative Pricing Error (ARPE) as the performance criterion, the empirical result reveals that the performance for GARCH is the best, and SV slightly dominates B-S. Additionally, this study performs the regression of ARPE on time-to-maturity, moneyness and a binary variable that is set to unity, if the option is a call and to zero in the case of a put. For the three models, the regression result displays that the pricing error is consistently decreasing in time-to-maturity and moneyness, and the out-of-sample performance in puts are more accurate than those in calls. Since the corresponding R2 of the regression in GARCH is the smallest, the pricing error for the other two models is relatively severe with respect to the three explanatory variables.