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研究生:莊蕙禎
研究生(外文):Hui-Chen Chuang
論文名稱:隨機跳躍下,具路徑相依之抗通膨保本票券的評價、避險和分析
論文名稱(外文):Valuation, Hedge and Analysis of Inflation-Protected and Principal-Protected Notes with Path Dependence in Jump Diffusion Model
指導教授:陳芬英陳芬英引用關係
指導教授(外文):Fen-ying Chen
學位類別:碩士
校院名稱:世新大學
系所名稱:財務金融學研究所(含碩專班)
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:56
中文關鍵詞:抗通膨保本票券隨機跳躍相對變數蒙地卡羅法控制變數蒙地卡羅法準蒙地卡羅法
外文關鍵詞:Inflation-protected and principal-protected notesJumpsAntithetic variates Monte Carlo methodControl variates Monte Carlo methodQuasi Monte Carlo method
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  近年來油價及各類民生物資的價格紛紛上漲,如何規避通貨膨脹風險在21世紀初成為世界關切的議題。本文擴展Brennan and Schwartz ( 1976 ) 和Chen ( 2007 ) 模型,並假設標的資產存在隨機跳躍現象,提出具路徑相依之抗通膨保本票券模型。該模型結合股權連結保本票券及抗通膨債券之特色,使該票券到期時,可以確保投資人之實質收益,亦可兼具保本之功效。並且在 ( 1 ) 股價與物價指數皆有隨機跳躍與 ( 2 ) 股價有隨機跳躍但物價指數無隨機跳躍兩種情況下,分別以普通蒙地卡羅法 ( ordinary Monte Carlo method )、相對變數蒙地卡羅法 ( antithetic variates Monte Carlo method )、控制變數蒙地卡羅法 ( control variates Monte Carlo method ) 與準蒙地卡羅法 ( quasi Monte Carlo method ) 模擬其合理價格與避險比例。結果發現,控制變數蒙地卡羅法之標準誤 ( standard error ) 最小且模擬所花費的時間最少。
Recently, high oil price becomes a concern. It is important for investors to protect their real profits from inflation risk. This paper expands the Brennan and Schwartz ( 1976 ) model and the Chen ( 2007 ) model, to present an inflation-protected and principal-protected model with jump diffusion. The model incorporates inflation-protected effect into principal-protected notes. At maturity, depending on inflation, investors can obtain the principal and capital gains. The article uses ordinary Monte Carlo method, antithetic variates Monte Carlo method, control variates Monte Carlo method and quasi Monte Carlo method to price the notes in two respects. First, both stock price and consumption price index have jump diffusion. Second, stock price exists jump diffusion but consumption price index doesn’t. In addition, we explore the delta hedge of the notes in the two scenarios. The results show that the standard errors by control variates Monte Carlo method simulation are lower than others. The method spends less time to simulate than the others.
第一章 緒論 1
  第一節 研究背景與動機 1
第二節 研究目的 2
第三節 研究架構 2
第二章 文獻回顧 5
  第一節 股權連結保本票券之研究 5
  第二節 抗通膨票券之研究 6
  第三節 跳躍擴散模型 7
第三章 研究方法 9
  第一節 資產隨機過程 9
  第二節 Cholesky分解法 10
  第三節 蒙地卡羅法 11
第四章 模型設定 17
  第一節 模型設定 17
  第二節 模型評價 20
  第三節 避險比例 30
  第四節 效率性分析 31
第五章 數值分析 33
  第一節 抗通膨保本票券合理價格之敏感度分析 33
  第二節 抗通膨保本票券避險比例之敏感度分析 34
  第三節 模型比較與分析 35
第六章 結論 37
參考文獻 45
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