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系統識別號 U0026-0812200911530184
論文名稱(中文) 利用均數複歸馬可夫模型評估公司債的信用風險
論文名稱(英文) Markov Model for Credit Risk with Mean-Reverting Transition Probabilities
校院名稱 成功大學
系所名稱(中) 財務金融研究所
系所名稱(英) Graduate Institute of Finance & Banking
學年度 94
學期 2
出版年 95
研究生(中文) 郭東霖
研究生(英文) Tung-Lin Kuo
電子信箱 u83020@yahoo.com.tw
學號 r8693120
學位類別 碩士
語文別 英文
論文頁數 72頁
口試委員 口試委員-劉裕宏
口試委員-黎明淵
指導教授-王澤世
中文關鍵字 馬可夫鍊  信用價差  違約機率  Vesicek 模型 
英文關鍵字 Markov model  Credit spread  Default probability  Vesicek model 
學科別分類
中文摘要 本文以Moody所發佈的2004年之一年期債券評等推移機率矩陣作為馬可夫(Markov)原始矩陣。並修正Kodera(2001)的模型,以國庫券利率代表總體經濟變數來取代其所原先設定的隨機變數,利用Vesicek 模型,估計未來20年的每年預期利率。接著,利用Bloomberg資料庫找出各種債信評等於2004年底的利率期間結構,藉以算出合理的債券價格。利用債券價格、回覆率及原始矩陣計算風險溢酬調整項,藉由風險溢酬調整項、利率預估值與原始矩陣的結合,便可計算在風險中立的情況下,未來各期間的債信評等推移矩陣。再由這些矩陣,找出債信評等轉移機率,也得以計算風險中立下的違約機率及信用價差。在違約機率與信用價差的估計方面,本文特別引進利率預估值,使得在評估未來的信用風險的過程中,也能夠考量當時的景氣概況。
英文摘要 The article showed the 1-year credit rating transition matrix which was published by Moody in 2004 and took it as an original matrix. The interest rates in this article were estimated by the Vesicek model for 20 years and were regarded as an important economic variable which would affect the credit risk. In order to calculate the reasonable bond price, we searched for the term structure of interest rates at each rating from the Bloomberg database. Then the bond price, recovery rate and original matrix could be used to evaluate the risk premium adjustment. We could make use of risk premium adjustment, the original matrix and the expected interest rates to evaluate the credit rating transition matrix in the risk-neutral world. From the matrix, we could get the credit rating transition probabilities, default probabilities and credit spreads of each rating. The contribution of the article was putting the expected interest rates into the Markov model. As a result, the economic condition would be considered while evaluating the credit risk.
論文目次 Contents

Chapter 1 Introduction…………………………………………………………….1
1.1 The Research Background and Objectives………………………………… 1
1.2 Structure of This Study………………………………………………………3

Chapter 2 Literature Review……………..………………………………………4
2.1 Credit Risk Modeling: Structural Approach………………………………4
2.2 Credit Risk Modeling: Reduced-form Approach………… ……………….9
2.3 Credit Rating Migration and Markov Chain……… … …………………13

Chapter 3 Methodology………………………….…………………………… …20
3.1 The Vesicek Model…………………………………………………………….20
3.2 The Markov Chain and Credit Rating Transition Matrix…… ……...21
3.2.1 The Real World Case………………..………………………… ………22
3.2.2 The risk-neutral world case………………………………………….24
3.3 The Rating Transition Probability and Risky Bond Price Evaluation……26
3.4 The estimation of risk premium adjustment………. ………………………..28
3.5 The calculation of credit spread………….……………… ………………….30

Chapter 4 Empirical Results.........................................32
4.1 Data selection……………………………………… ……………………….32
4.2 The Analysis of Market Data……………………………… ……………..33
4.2.1 The Term Structure of Risky Bonds and Default-free Bond ……33
4.2.2 The Credit Spreads………………………………………… ………….36
4.3 The Estimation of Interest Rate…………………………… …………..38
4.3.1 The Parameters of Vesicek Model…………………… ………………38
4.3.2 The Interest Model……………………………………………………..39
4.4 The Evaluation of Bankruptcy Process…………………………………..41
4.4.1 The Estimation of Important Variables…………………………….41
4.4.2 The Original Credit Rating TransitionMatrix.................43
4.4.3 The Evaluation of Risk Premium Adjustment…………… …………45
4.4.4 The Credit Rating Transition Matrix…………… …………………49
4.5 The Evaluation of Credit Spreads…………… …….. … … … ….53
4.5.1 The Credit Spreads of Model and Bond’s Yield………………….53
4.5.2 The Influence of Interest Rate on Credit Spreads…… ……….58

Chapter 5 Conclusions and Further Researches…………………………..…62
5.1 Conclusions……………………………….………. ………………………..62
5.2 Further Researches……………………………………………………………63

Reference………………………………...…………………………………………64
Appendix A The discrete-time Vesicek Model……………… …………….66
Appendix B The Credit Rating Transition Matrix (Risk-neutral)………67


List of Tables

Table 4.1 The Term Structure of Risky Bond and Default-free Bond …….……33
Table 4.2 The Term Structure of Risky Bonds and Default-free Bond after
Interpolating …..34
Table 4.3 The Market value of Bonds……………………………………… …………35
Table 4.4 The Term Structure of Credit Spreads ………………..… ……………36
Table 4.5 The Estimation of the parameters in Interest Rate Model………….39
Table 4.6 The Expected Interest Rates……………………………………………...40
Table 4.7 The Implied λ Value from the Market Price of Bond…………….……42
Table 4.8 The Result of Regression Analysis………………… ……………………43
Table 4.9 The one-year Credit Rating Transition Matrix in 2004…… ……….44
Table 4.10 The Adjusted one-year Credit Rating Transition Matrix in 2004…44
Table 4.11 The estimation of π value…………………………………… ………….46
Table 4.12 Accumulated Default Probabilities in the Risk-neutral World……51
Table 4.13 The Estimated λ Value………………………………………………………53
Table 4.14 The Evaluation of Credit Spreads…………… …………………………54


List of Figures

Figure 4.1 The Credit Spread Curves at Dec31, 2004 (Aaa~Baa)…………………37
Figure 4.2 The Credit Spread Curves at Dec31, 2004 (Ba~Caa) ………………..37
Figure 4.3 The Expected Interest Rates………………………………………………40
Figure 4.4 The estimated π value for 20 years (Aaa) ………………………… .47
Figure 4.5 The estimated π value for 20 years (Aa)………… ………………….47
Figure 4.6 The estimated π value for 20 years (A)……………… ………………47
Figure 4.7 The estimated π value for 20 years (Baa) …………………………..48
Figure 4.8 The estimated π value for 20 years (Ba)……………………………..48
Figure 4.9 The estimated π value for 20 years (B) ……………………………..48
Figure 4.10 The estimated π value for 20 years (Caa)…………………………..49
Figure 4.11 Accumulated Default Probabilities in the Risk-neutral World (Aaa to Baa)…….52
Figure 4.12 Accumulated Default Probabilities in the Risk-neutral World (Ba to Caa)……..52
Figure 4.13 The Evaluation of Credit Spreads ………………………………….....55
Figure 4.14 The Credit Spreads of Model and Market Value of Bonds (Aaa) …..55
Figure 4.15 The Credit Spreads of Model and Market Value of Bonds (Aa)……..56
Figure 4.16 The Credit Spreads of Model and Market Value of Bonds (A) ……..56
Figure 4.17 The Credit Spreads of Model and Market Value of Bonds (Baa) …..56
Figure 4.18 The Credit Spreads of Model and Market Value of Bonds (Ba)……..57
Figure 4.19 The Credit Spreads of Model and Market Value of Bonds (B) ……..57
Figure 4.20 The Credit Spreads of Model and Market Value of Bonds (Caa) …..57
Figure 4.21 The Influence of Interest Rate on Credit Spreads (Aaa Rating)...59
Figure 4.22 The Influence of Interest Rate on Credit Spreads (Aa Rating)…..59
Figure 4.23 The Influence of Interest Rate on Credit Spreads (A Rating).…..59
Figure 4.24 The Influence of Interest Rate on Credit Spreads (Baa Rating)...60
Figure 4.25 The Influence of Interest Rate on Credit Spreads (Ba Rating)…..60
Figure 4.26 The Influence of Interest Rate on Credit Spreads (B Rating).…..60
Figure 4.27 The Influence of Interest Rate on Credit Spreads (Caa Rating)...61
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