本文的目的在於建立一套有效率的交易策略，一般選擇權市場會使用的定價公式為Black-Scholes(1973) ，這樣的假設下無法捕捉波動率的隨機過程(Stochastic nature of volatility)與資產報酬的群聚現象(Correlation between volatility and spot return)，所以本文將使用GARCH Option Model與傳統的Black-Scholes Model做比較，並驗證其是否會優於Black-Scholes Model。
先前的Heston-Nandi由於沒有封閉解而沒有辦法有效率的定價，本篇研究依循Heston and Nandi(2000) 帶有封閉解的GARCH Option Model，以Heston and Nandi不同於一般的GARCH(1,1)捕捉市場的波動率。根據台指選擇權的實證結果顯示，特別是在價外與價平時，Heston & Nandi價格比較接近市場價格，而在深價內時，三者並沒有太大差異，整體來說，使用GARCH Option Model可以獲得較好的交易策略。

This article aims to build an efficient trading strategy. The pricing formula Black-Scholes(1973)
Is widely used in the option market. However, the hypothesis of Black-Scholes is incapable of capturing the stochastic nature of volatility and correlation between volatility and spot return. Therefore, this article will compare GARCH Option Model with traditional Black-Scholes Model to see whether the former is better than the later. Heston-Nandi cannot provide an effective pricing strategy because it is lack of close form. This article will comply with Heston and Nandi(2000) and the close form of GARCH Option Model, to capture the market volatility with Heston and Nandi different from regular GARCH(1,1). According to the result shown in the option in Taiwan market, the price of Heston & Nandi is closer to market price especially when it is out of price and at the money. When it is deep in the price, there is no significant difference within the three models. Overall, GARCH Option Model can provide better trading strategy.

摘要
目 錄
壹、 緒論………………………………………………………………………………………….1
一、 研究動機……………………………………………………………………………………1
二、 研究目的……………………………………………………………………………………1
三、 研究方法……………………………………………………………………………………1
四、 研究架構……………………………………………………………………………………2
貳、 文獻回顧………………………………………………………………………...…………3
第一節、 Black-Scholes Model選擇權理論價格…………………………………3
一、 隱含波動率………………………………………………………………….......………3
二、 GARCH(1,1)波動率模型……………………………………………........…………3

參、 GARCH 估計模型……………………………………………………………….………4
第一節、 Heston & Nandi GARCH Option Pricing Model…………..….……4
一、 模型設定與假設………………………………………………………………….………4
二、 最大概似估計法(MLE) ………………..………………………………………………7

肆、 實證分析……………………………………………………………………….……………7
第一節、 台指選擇權及資料簡介…………………………………………………………7
一、 台指選擇權簡介…………………………………………………………..........………7
二、 資料來源………………………………………………………………….........….………8
三、 研究期間……………………………………………………………….......……...………8
第二節、 模型參數估計與歷史波動度………………………………………..…………9
第三節、 蒙地卡羅模擬H-N GRACH Model….. ……………..…………...………10
第四節、 選擇權價格比較…..……………………………………………….…….……….11
伍、 結論與建議…..…………………………………………………………………………….14
一、 結論…..…………………………………………………………………………….………..14
二、 建議…..………………………………………………………………………………….…..14
參考文獻…. …..……………………………………………………………...………………....15

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