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研究生: 林美婷
Lin, Mei-Ting
論文名稱: 與股價連結的結構債之價值與風險
The Value and Risk of a Stock Price-linked Structured Notes
指導教授: 沈士育
Shen, Shih-Yu
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2011
畢業學年度: 100
語文別: 中文
論文頁數: 40
中文關鍵詞: 結構債障礙選擇權邊界積分法熱傳導方程式
外文關鍵詞: structured notes, barrier option, boundary integral method, heat equation
相關次數: 點閱:102下載:5
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  • 本文利用邊界積分法解一連續式單邊界的結構債定價問題,首先介紹結構債、選擇權以及障礙選擇權,接著以Black-Scholes Model為數學模型,將其轉換成熱傳導方程式的邊界值問題,再利用邊界積分法解此邊界值問題,並解得結構債價格、波動率以及碰觸上限價格的機率。
    本文數值計算部份使用Visual C++程式語言計算,再利用數學軟體Matlab繪製圖形。

    In study, a boundary integral method is designed to deal with single touch barrier structured notes. First the pricing of structured notes﹑option and barrier option are introduced. The black-scholes model is converted to a heat equation boundary value problem. Then use a boundary integral method to deal with the boundary value problem and solve the price of structured notes﹑volatility and probability of touch barrier.
    In study, the method is implemented with Visual C++ and Matlab.

    第一章 緒論-----------------------1 1.1 結構債簡介-------------------1 1.2 選擇權與障礙選擇權簡介---------5 1.3 文獻回顧---------------------8 1.4 章節大綱--------------------10 第二章 數學模型與邊界值問題--------12 2.1 Black-Scholes Model-----12 2.2 Heat Equation邊界問題-------16 2.3 積分表現式------------------18 2.4 Green’s functuon-----------22 2.5 機率密度函數----------------24 第三章 數值法與結果---------------27 3.1 隱藏波動率------------------27 3.2 結構債價值------------------32 3.3 碰觸界限價格機率-------------34 第四章 結論---------------------37 參考文獻-------------------------39

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