B-S模式與隨機波動性定價模式之比較：臺指選擇權之實證

A Comparison between B-S Model and Stochastic Volatility Option Pricing Models: Empirical Evidence from TAIEX Options

B－S模式與其修正模式，如隨機波動性模式、隨機利率模式模式、隨機波動性與跳躍擴散模式等，孰優孰劣？國內許多對不同市場的實證研究，大多顯示修正的模式績效優於B－S模式。由於臺灣股價指數選擇權是一種嶄新的金融商品，其價格行為受到學術界與實務界的關心，但到目前為止文獻上尚未有所評估。因此本文以臺指選擇權為標的，採用B－S模式、Hull & White （1987）模式及Heston （1993）模式等三種模型分別配合歷史波動生與GJR GARCH波動性，對臺指選擇權進行實證研究，比較理論與實際價格之誤差，並進行誤差原因的分析，實證結果顯示，對近月份臺指選擇權，雖然以平均絕對誤差為指標時，並無單一模式永遠優於其他模式，但若以百分比誤差及均方根誤差為指標時，則B－S模式似乎優於其他模式。但對遠月份選擇權，三種誤差指標均顯示隨機波動性選擇權定價模式優於B－S模式。這對投資人有很重要的投資意涵。至於各模式之定價誤差與選擇權價內程度、距離到期日時間、標的股價指數變動率、及股價波動性等因素存在有顯著的關聯性。

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) model 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 factors. Such as in-the-money, time to maturity, percentage change in stock index, and the volatility of the underlying index.