臺灣博碩士論文加值系統

本研究採用邊界元素法來解決有報償之連續式雙邊界障礙選擇權定價之問題，即當在到期日前，若標的股價碰到上限價格或下限價格時，選擇權立即失效，但賣方會支付給買方一筆報償。

在本文中，首先是回顧選擇權、障礙選擇權及雙邊介障礙選擇權。接著，作者以Black-Scholes Model為其數學模型，將其轉換成熱方程式的邊界值問題，進而利用邊界元素法來處理此邊界值問題，並解得有報償之連續式雙邊界障礙選擇權的價格。

最後，針對履約價格、波動率等各參數做敏感度分析。

This study, a boundary element method is designed to deal with double touch barrier options with rebate. That is, a dobule touch barrier call is knocked out
when the price reaches the upper or lower barreir before expiration day, but the seller have to pay rebate to buyer.

In this thesis, first the pricing of option、barrier option and double barrier option are reviewed.
The black-scholes model is converted to a heat equation boundary value problem.
Then use a boundary element method to deal with the bounday value problem and solve the price of continuous double barrier options with rebate.

Finally,some sensitive analysis are present.

第一章 緒論

1.1 股票選擇權簡介 ...........1
1.2 障礙選擇權簡介 ...........3
1.3 雙障礙選擇權簡介..........5
1.4 文獻回顧..................7
1.5 章節大綱..................9
第二章 數學模型與邊界值計算

2.1 Black-Scholes Model....10
2.2 雙邊界障礙失效買權與邊界值問題 12
2.3均質方程轉換過程......13
2.4邊界積分表現式與邊界積分方程....15
2.5邊界元素法.....22
2.6 雙邊界障礙選擇權之價格.......32

第三章數值例

3.1數值方法的準確性......36
3.2雙邊界障礙買權和一般歐式買權之比較..41
3.3 敏感度分析.....45

第四章 結論.....50
參考文獻.....52

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