臺灣博碩士論文加值系統

由過去的歷史經驗可知對於經濟預測是件艱辛的工作，尤其是對於因為突發事件所引起的股市崩盤更是無法預測的，例如：，在西元1995至2005年十年期間，平均每年大約有2到3次突發事件引發股市重挫，1999年台灣地區發生921集集大地震，在限制跌幅為3.5%的情況下，27日指數下跌212.21點，跌幅依舊高達2.66%、2000年10月3日政府宣布核四停建，政經情勢變化，指數下跌145.52點，跌幅爲2.37%、2000年11月國內金融風暴及罷免總統案，20日指數下跌322.14點，跌幅爲6.23%、2001年9月11日美國紐約世貿中心遭受恐怖份子攻擊，次日台灣休市一天，然13日指數依舊下跌224.44點，跌幅爲5.37%，14日指數下跌177.87點，跌幅爲4.50%。雖然目前沒有任何的經濟學說是可以準確預測股市的崩盤，但是在市場變動之前我們仍然可以用數學模型來感測迫在眉睫的變動，在崩盤前，事先建立一個避險投資組合，以規避不可預測之經濟崩盤。
避險時必須決定對於資產組合要用多少股票來保護，亦即必須決定資產組合與股票部位之搭配比率，此即一般所謂之避險比率。為說明避險比率之計算方法，本文假設股票組合避險部位之報酬與波動完全相同，為使股票避險部位後之投資組合的風險最小，在本文中主要使用Hua與Wilmott(1997)所定義之Crash模型進行分析，嘗試在發生嚴重崩盤的情況下，我們如何使用穩定的避險，迫使投資組合的風險值損失減少到最低，以符合現實情況。研究Crash模型的衍生性金融商品透過連續避險策略不斷調整其避險部位，計算出發行時選擇權的定價、找出最理想的避險比率以及最糟可能情況時的價值，以四種不同方式的避險策略，找出最佳的避險部位，計算出最佳發行時選擇權的定價為研究主旨，我們利用單期Crash模型和疊代的方式找出 期Crash模型的分析架構。

It is very challenging to forecast the volatile economic event with the past experience. It is unfortunate that experts could not forecast the stock market collapse before the event. Between 1995 and 2005, there were two to three startling events causing the stock market to fall significantly . In the serious earthquake 921 in Taiwan in 1999, the government limited the fall range to 3.5%. The stock index went down 212.21 points on September 27, the first day that the stock exchange restored, and the fall range was 2.66%. On October 3, 2000, the government declared to stop building the nuclear power plant No. 4. The dramatic changed policy caused the stock index to plunge 145.52 points , and the fall range was 2.37%.Due to the financial windstorm and the case of impeaching the President in November 2000, the stock index fell 322.14 points on November 22, and the fall range was 6.23%. In the terrible 911 attack on the United States in year 2001, the Taiwan government declared to close the stock exchange for one day on September 12. The stock index plummeted 224.44 points on September 13, and the fall range was 5.37%. The stock index continued to plunge 177.87 points on September 14, and the fall range was 4.5%.There is no economic model to forecast correctly the fall range in the stock market, although we can develop some models in mathematics to forecast the imminent variation before the stock index declines to avoid unanticipated hardships.
The hedge is to decide how many stocks can protect the holding portfolio. The ratio of the investment combination to the holding stock is called the delta-hedge. In order to explain the calculation method of the delta-hedge, we assume that the delta-hedge and the stock combination’s rewards are the same. Controlling the lower risks of the delta-hedge, we analyze and apply the Crash model developed by Hua & Wilmott (1977). When the stock market index falls substantially, we would like to know how we can use the steady hedge method to cut down the loss and lower risks for the investment group. To analyze the Crash model through the continuous hedge tactic to adjust the delta-hedge, we can calculate the issue price of the option and find the perfect hedge ratio and the worse value that they could be. There are four kinds of the hedge tactic to find the best delta-hedge. The purpose is to calculate the best issue price of the option.

致 謝 詞…………………………………………………………………I
中文摘要………………………………………………………………II
英文摘要………………………………………………………………III
目 錄…………………………………………………………………V
圖 目 錄……………………………………………………………VIII
表 目 錄………………………………………………………………X
第一章 緒　論………………………………………..….………1
1.1　　研究動機……………………………………….…….1
1.2　　研究目的………………………………….……………2
1.3　　研究架構…………………………………………….…4
第二章 選擇權之簡介……………………………….……………5
2.1 選擇權歷史……………………………………..……5
2.2 選擇權的意義…………………………………..……5
2.3 選擇權的類型……………………………..…………6
2.3.1 買權與賣權區分…………………………………6
2.3.2 歐式選擇權與美式選擇權區分…………………9
2.4 影響選擇權價格的因素…………………..…………9
2.4.1 影響選擇權價格的因素包括…………………9
2.4.2 履約價格………………………………………9
2.4.3 資產價格……………………………………10
2.4.4 到期時間……………………………………10
2.4.5 股價波動率…………………………………10
2.4.6 利率…………………………………………11
2.5 指數選擇權可依履約價格分為價內、價平、價外…11
2.5.1 價內選擇權……………………………………11
2.5.2 價平選擇權……………………………………11
2.5.3 價外選擇權……………………………………12
2.6 內含價值與時間價值…………………………………12
第三章　　二項式選擇權評價模型…………………………………15
3.1 二項式模型的簡介……………………………………15
3.2 二項式模型的假設……………………………………16
3.3 單期二項式模型………………………………………18
3.4 兩期二項式模型………………………………………22
3.5 多期二項式模型………………………………………25
第四章 Black-Scholes選擇權評價模型…………………………26
4.1 Black-Scholes模型的簡介………………….………26
4.2 Black-Scholes模型假設……………………………27
4.3 Black-Scholes買權評價公式………………………27
4.4 Black-Scholes賣權評價公式………………………31
　　　4.5 二項式模型與Black-Scholes模型的關係…………31
4.6 跳躍擴散模……………………………………………32
第五章 Crash模型…………………………….…………………34
5.1 Crash模型上的避險及定價…………………….……34
5.2 Crash 模型假設………………………………………35
5.3 Crash模型的避險投資組合…………………….……37
5.4 單期Crash模型下選擇權的定價及避險……………40
5.4.1 持有一單位的call和賣空 數量的股票……40
5.4.2 賣出一單位的call和持有 數量的股票……46
5.4.3 持有一單位的put和持有 數量的股票………52
5.4.4 賣出一單位的put和賣空 數量的股票………58
5.5 多期Crash模型下選擇權的定價及避險……………66
第六章 結論………………………………………………………79
6.1 結論…………………………………………………79
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