臺灣博碩士論文加值系統

在實證上，常發現利率存在自我相關情況。本篇論文主要貢獻，是延伸Liao and Chen (2006)之一階移動平均(continuous-time type of first-order moving average process, 以下簡稱MA(1))單因子模型，結合Heath, Jarrow, and Morton (1992)(簡稱HJM)遠期利率模型設定，假設遠期利率為MA(1)之多因子模型，於遠期平賭測度下，推導出MA(1)型態之零息債券選擇權封閉解。本研究主要貢獻在於：(1) 當遠期利率為MA(1)過程時，即期利率與零息債券過程亦有MA(1)效果。(2) MA(1)型態之零息債券選擇權公式解與HJM之零息公債選擇權相似，主要差異在於波動度輸入參數受到MA參數影響。最後，藉由數值分析可知，當利率存在自我相關情況下，零息債券選擇權價值受到MA參數影響極大。(3) 利用Jamshian(1989)模型架構，MA(1)參數對於付息債券選擇權公式解之影響也明顯可見。

Under forward martingale measure, by extending Heath, Jarrow, and Morton (1992) and Liao and Chen (2006), this paper derive the closed-from solution for a European zero coupon bond option when the forward rate follows a continuous-time type of first-order moving average process. Different from the one factor model of Liao and Chen, we propose a multiple factors forward rate model of MA(1)-type process. The pricing formula of ZCB options is similar to that of HJM formula except for the volatility input which is function of MA parameter. Based on the numerical analyses, the impact of autocorrelation induced by MA(1)-type process is significant to option values.

摘 要 ii
Abstract iii
誌 謝 iv
目 錄 v
表目錄 vii
圖目錄 viii
第壹章 緒論 1
第一節 研究背景、動機及目的 1
第二節 研究架構 3
第貳章 文獻回顧 5
第一節 傳統利率期間結構模型 5
第二節 近代利率期間結構模型 7
第三節 實證研究 9
第參章 研究方法 10
第一節 HJM利率模型假設及介紹 10
第二節 MA(1)下遠期利率模型 13
第三節 風險中立測度下之平賭特性 16
第四節 債券選擇權評價 20
第五節 付息債券選擇權評價 22
第肆章 數值分析解 25
第一節 零息債券選擇權評價數值分析解 25
第二節 付息債券選擇權評價數值分析解 27
第伍章 結論 29
附錄 30
附錄一 即期機率測度轉換 30
附錄二 遠期機率測度轉換 32
附錄三 付息債券選擇權推導 34
參考文獻 36

一、中文
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