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研究生:林德政
研究生(外文):Te-cheng Lin
論文名稱:隨機利率下 Lévy 過程在信用風險之應用:結構式模型
論文名稱(外文):The Application of Lévy Processes with Stochastic Interest Rates in Structural Models
指導教授:林士貴林士貴引用關係
指導教授(外文):Shih-kuei Lin
學位類別:碩士
校院名稱:國立高雄大學
系所名稱:亞太工商管理學系碩士班
學門:商業及管理學門
學類:企業管理學類
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:89
中文關鍵詞:跳躍擴散模型Lévy過程Esscher transform馬可夫調整普瓦松過程
外文關鍵詞:Jump-diffusion processEsscher transformLevy processMarkov modulated Poisson Process
相關次數:
  • 被引用被引用:0
  • 點閱點閱:165
  • 評分評分:
  • 下載下載:31
  • 收藏至我的研究室書目清單書目收藏:0
Merton (1976)提出跳躍擴散模型評價有風險債券,假設擴散部分代表系統風險,而跳躍部分代表公司特有風險,成為結構式模型的主軸。然而Jarrow and Rosenfeld (1984)與Kim et al. (1994)經過實證發現,跳躍部分主要為系統風險。本文假設資產動態過程為L�臀y過程,利率為隨機,同時放寬跳躍部分為系統性風險,採用Esscher transform 處理機率測度的轉換,計算負債價值與違約機率。另外跳躍頻率也進一步假設,由原本的普瓦松過程放寬為馬可夫調整普瓦松過程。數值分析結果發現在跳躍頻率服從普瓦松過程之下,隨著負債到期日的增加,跳躍幅度的平均值、變異數、跳躍頻率與負債價值呈現負相關,與違約機率呈現正相關。在跳躍頻率服從馬可夫調整普瓦松過程之下,越容易停留狀態之跳躍頻率,對於負債價值的影響越大。本文模型計算負債價值與違約機率,可適用於系統風險造成資產價值發生跳躍,例如美國次級房貸風暴,亦可在不同跳躍頻率的情況之下使用。
In jump-diffusion process, jump component is supposed to reflect non-systematic risk. In terms of CAPM, this means that the jump risk is not priced. However, Jarrow and Rosenfeld (1984) and Kim et al. (1994) document that jump component mainly represent systematic risk. In this paper, we not only suppose the jump risk is non-diversifiable but also model the firm value as the exponential of a L�臀y process. Assuming jump risk is systematic will need the well-established technique, Esscher transform for change of measure. In particular, we set the arrival of new information may be modeled by Markov modulated Poisson Process and adopt the Vasicek stochastic interest rate model. Our model can price risky debt under different jump intensity when jump risk is systematic, like subprime mortgage crisis.
目錄
第一章 緒論----------------------------------------------------1
第二章 文獻探討------------------------------------------------4
第一節 信用評分模型--------------------------------------------4
第二節 結構式模型----------------------------------------------6
第三節 縮減式模型---------------------------------------------13
第四節 信用評等移轉模型---------------------------------------15
第五節 L�臀y 過程----------------------------------------------18
第三章 研究方法-----------------------------------------------20
第一節 模型設定-----------------------------------------------20
第二節 跳躍風險可分散-----------------------------------------22
第三節 跳躍風險不可分散---------------------------------------30
第四章 數值分析-----------------------------------------------37
第五章 結論與建議---------------------------------------------45
參考文獻------------------------------------------------------46
附錄----------------------------------------------------------52
參考文獻
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