自Black and Scholes (1973)發表了著名的選擇權定價模型之後，選擇權的定價理論成為學術界的研究重心，因Black and Scholes 模型簡化的假設引發後續研究對於B-S模型的修正，如隨機波動性模型、隨機利率模型、隨機波動性與跳躍擴散模型等等。對於這些修正模型是否優於B-S模型的議題，國內外許多學者在不同市場的實證探討，大多顯示修正的模型績效優於B-S模型。
由於台灣股價指數選擇權對國內投資人而言，是一種新的金融商品，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，因此本研究以台灣股價指數選擇權為標的，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性與GJR GARCH波動性，對台灣股價指數選擇權進行實證研究，衡量及比較理論價格之誤差，並進行誤差原因的分析。本文的實證結果指出：
1.遠月份台股指數選擇權之平均絕對誤差(MAE)與均方根誤 差(RMSE)，其最小誤差絕大多數出現在Heston (1993)模型配合歷史波動性之模式上。
2.近月份台股指數選擇權在深度價內、價內與價平等價位，所有的模型配合各種波動性均高估了市場的價格；至於價外與深度價外選擇權，平均而言各種模式的理論價格高估了市場價格。
3.對近月份台股指數選擇權，B-S模型配合歷史波動性為最佳模式，Heston (1993)模型配合GJR GARCH波動性為最差之模式。
4.對遠月份台股指數選擇權，Heston (1993)模型配合歷史波動性為最佳之模式；Hull & Wtite (1987)模型配合GJR GARCH波動性為最差之模式。
5.GJR GARCH波動性模型並未優於歷史波動性模型、隨機波動性模型並未優於B-S模型。
6.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「波動性」等因素存在有顯著的線性關係。

Since 1973 Black and Scholes published the famous option pricing model, option pricing theory has become an academic research focus. As a result of many unduly simplified assumptions of the B-S model, many scholars started to modify the B-S model, such as the “stochastic volatility option model”, “stochastic interest rate option model” and “stochastic volatility and poisson jump diffusion option model”. Many scholars devoted themselves to investigate the issue about whether the free-restricted models outperform the B-S model. Most empirical results indicated that the free-restricted models outperform the B-S model.
Since the stock index option is a new financial derivatives in Taiwan, the pricing behavior of stock index options is concerned by investors as well as academic workers. However, up to date, the pricing behavior of index options has not been found in the literature. This study will bridge this gap. This study investigates the B-S, Hull & White (1987) and Heston (1993) models with historical and GJR GARCH volatilities on “the Taiwan Stock Exchange Capitalization Weighted Stock Index Options.” In particular, this study measures and compares the pricing biases between theoretical and market prices, and proceeds to analyze the cause to pricing biases. The empirical results indicate that:
1.For far month TAIEX Options, the smallest MAE and RMSE pricing errors take place on Heston (1993) model with historical volatility.
2.For near month TAIEX Options, all models with two kinds of volatility seem to overprice deep-in-the-money, in-the-money and at money options. However, all models with two kinds of volatilities seem to underprice out-of-the-money and deep-out-of-the-money options.
3.For near month TAIEX Options, the B-S model with historical volatility outperforms any other models; however, Heston (1993) model with GJR GARCH volatility seems to be the poorest model.
4.For far month TAIEX Options, the Heston (1993) model with historical volatility seems to be the best model; however, the Hull & White (1987) model with GJR GARCH volatility seems to be the poorest model.
5.GJR GARCH volatility does not seem to outperform historical volatility and stochastic volatility option pricing model does not seem to outperform the B-S model.
6.For all option pricing models, the pricing errors are systematically related to the extent to which the options are in-the-money, time to maturity, percentage change in stock index, and the volatility of the underlying assets.

一、中文部分
1.何桂隆(1998)，不同波動性估計方法下台灣認購權證評價績效之比較，成功大學企業管理研究所未出版碩士論文。
2.林佩蓉(2000)，Black-Scholes 模型在不同波動性衡量下之表現－股價指數選擇權，東華大學企業管理研究所未出版碩士論文。
3.林敦舜(2002)，台灣認購權證評價之研究－探討二項式及三項式樹狀模型之評價差異，交通大學經營管理研究所未出版碩士論文。
4.周行一、陳怡雯(2002)，「台灣證交所發行量加權股價指數未納入現金股利之再投資因素對投資報酬率及基金績效衡量之影響」，證券市場發展季刊，第14卷第1期，pp. 1-24。
5.洪啟安(1998)，台灣認購權證價格形成之實證研究，長庚大學管理學研究所未出版碩士論文。
6.陳香君(2001)，隨機波動選擇權評價模型之實證－以臺灣認購權證為例，高雄第一科技大學財務管理研究所未出版碩士論文。
7.張文騰(2001)，以電子業為標的之台灣認購權證評價研究－AMM, CRR與B-S模型之比較，輔仁大學管理學研究所未出版碩士論文。
8.黃大展(2001)，隨機波動下的二元樹狀模型之探討，政治大學財務管理研究所未出版碩士論文。
9.楊玉菁(2001)，台灣個股型認購權證評價之研究，彰化師範大學商業教育研究所未出版碩士論文。
10.趙其琳(1999)，波動性預測能力比較—台灣認購權證之實證研究，淡江大學財務金融研究所未出版碩士論文。
11.蔡立光(1998)，台灣上市認購權證定價模型與避險策略之研究，中央大學財務管理研究所未出版碩士論文。

二、英文部分

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