B-S模式與隨機波動性定價模式之比較：台指選擇權之實證

Abstract

Whether the modified option pricing models (such as stochastic volatility option model, stochastic interest rate option model, and stochastic volatility and Poisson jump diffusion option model) outperform the B-S model is an important issue in finance. Most empirical results indicated that stochastic volatility models outperform the B-S model. Since the Taiwan stock index option (TAIEX option) is a new financial derivative, the pricing of this option is concerned by investors as well as academic workers. However, up to date, the pricing behavior of TAIEX options has not been found in the literature. This paper will bridge this gap. We compare the relative performance of B-S, Hull & White (1987) and Heston (1993) models with historical and GJR GARCH volatilities, respectively, in evaluating TAIEX options, and analyzes the factors of pricing biases. Empirical results indicate that, for near month options, although none of the pricing model superiors to other models using mean absolute errors, the B-S model seems to be better than the other models by using mean percentage errors and root mean square errors. For far month options, stochastic volatility models are better than the B-S model by using three measures of errors. These results have an important implication to investors. Finally, the pricing errors are significantly related to factors, such as in-the-money, time to maturity, percentage change in stock index, and the volatility of the underlying index.