Copula模型在信用連結債券的評價與實證分析 - 政大學術集成
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(3) Factor Copula. Copula. Copula 18. Copula Model. Factor Copula Model. ii.
(4) ABSTRACT Value of the credit-linked notes depend on the pool of assets whether default or not, so the promised payoff of credit-linked notes is affected by other risky underlying assets. Therefore, how to estimate the probability of default asset pool accurately and objectively will be a very important issue. In the past literature, researchers usually use given parameters, and assume assets probability of default are independent from each other under valuation. Furthermore, it is not obvious to capture the joint probability of default. Thus, this article extends the Factor Copula Model to provide a new methodology of pricing credit-linked notes, which consider the default correlation between the extent of assets in order to achieve result in line with market and with Factor Analysis method added, trying to figure out the impact of commodity price factor behind the market. In the empirical analysis, pricing the actual commodity issued by LB Baden-Wuerttemberg using extend model and Copula model, we found that no matter choose in-the-sample or out-the-sample data to valuation, the models in this article are superior to Copula model by compare the root-mean-square deviation(RMSE). It means add the market factors into our valuation is beneficial. In terms of selection factors, we select eighteen factors prepared by Morgan Stanley Capital International, and three categories of factors may be extracted from Factor Analysis method. By observing RMSE, both national factors and industry factors will influence on the commodity, but world factors not only did not significantly impact on the commodity, but also add it to calculate the expected price further from the market price. Representative said not blind join the many factors can make the model to calculate the price close to the market price, it is a factor depending on the degree of influence of the added asset. For the suggestion of future research. The fact that the presence of empirical iii.
(5) assumptions in this study, result in the evaluation process is not entirely realistic to market situation. We suggest to get the real data on the market or use random way to calculate, we believe that the outcome will be closer to the market price. Meanwhile, by selecting different factors to evaluate, trying to discover further factors which significantly impact on the commodity; it will help us better to understand the factors behind the commodity, so investors can predict commodity future prices by observing the market data.. Key Words: Credit Risk, Copula Model, Factor Copula Model, Credit-Linked Notes. iv.
(6) ...........................................................................................................# ....................................................................................................................................i .......................................................................................................................... ii ABSTRACT .................................................................................................................... iii ...................................................................................................................................v ............................................................................................................................ vii ........................................................................................................................... viii Chapter 1. ............................................................................................................1. 1.1. ....................................................................................................1. 1.2. ........................................................................................................2. 1.3. ........................................................................................................3. Chapter 2. ....................................................................................................4. 2.1. (CLN). ..............................................................................4. 2.2. ........................................................................................6. 2.3. ................................................................................9. Chapter 3. Copula. ............................................................................11. 3.1. Copula...........................................................................................................11. 3.2. Gaussian Factor Copula.......................................................................13. 3.3. ..................................................................................................14. 3.4. ......................................................................................................15. 3.5. ..................................................................................................16 v.
(7) Chapter 4 4.1. .................................................................................18 Copula. ......................................................................................................18 Gaussian Factor Copula. 4.2 Chapter 5. ..............................................................19. ..................................................................................................22. 5.1. ..................................................................................22. 5.2. ..............................................................................................23. 5.3. ..............................................................................................24. 5.4. ..............................................................................................28. Chapter 6. .............................................................................................32. 6.1. ..............................................................................................................32. 6.2. ..........................................................................................34 .........................................................................................................................35. .................................................................................................................................37. vi.
(8) 2-1. ......................................................................................9. 5-1. ................................................................................................22. 5-2. ....................................................................................................23. 5-3. ............................................................................................24. 5-4. ....................................................................................25. 5-5. Copula. 5-6. Factor Copula. 5-7. In-Sample. 5-8. Out-The-Sample. 5-9. In-Sample. 5-10. Out-The-Sample. ............................................................26 .................................................27 .......................................................................28 ............................................................29 ..............................................................................31 ...................................................................31. vii.
(9) 1-1 2-1. ........................................................................................................3 CLN. ...................................................................................................4. 2-2. ................................................................5. 2-3. ........................................................................................5. 2-4. ........................................................................................................6. 2-5. ........................................................................................................6. 3-1. ......................................................................................................15. 4-1. Gaussian Factor Copula. 5-1. In-Sample. 5-2. Out-The-Sample. ...............................................................19 .........................................................30 .............................................30. viii.
(10) Chapter 1 1.1. 1.
(11) 1.2. 2.
(12) 1.3. 1-1 3.
(13) Chapter 2 (Credit-Linked Notes CLN). 2.1. (CLN). 2-1. CLN. 4.
(14) 2-2. 2-3. International Swaps and Derivative Association( ,ISDA). 5.
(15) 2-4. 2-5. 2.2. CreditMeticsTM KMV Credit Risk Plus. Credit Portfolio View. 6.
(16) 7.
(17) 8.
(18) 2-1. 2.3. 9.
(19) 10.
(20) Chapter 3 3.1. Copula. Copula Copula (Uniform distribution). 1. 2.. C. 3.. C. Sklar’s n Copula. (dependent structure). ,. Copula. Copula (co-movement). (. ). , i=1,2,…,n 11.
(21) ( …). (Copula. ). Copula. Copula. Copula 1.. Gaussian Copula Gaussian Copula Copula. 2.. Student-t Copula Copula. Student-t 3.. Archimedean Copula Clayton-n-Copula. 12.
(22) Gumbel-n-Copula. Frank-n-copula. 3.2. Gaussian Factor Copula. Gregory and Laurent Factor copula. Copula. 13.
(23) Copula. Factor Copula. Copula Gaussian Student-T. Student-T. Copula. 3.3. 14. Factor.
(24) 3.4. Common Factor Unique Factor. 3-1. Principal Component Method Principal Factors Analysis. Maximum Likelihood Method. 15.
(25) 3.5 i. i. t. t. i. i i i 16. t t.
(26) t. t. 0. t. t. 17.
(27) Chapter 4 4.1. Copula Copula. Copula. Gaussian Copula. Pearson. CLN. 18.
(28) 4.2. Gaussian Factor Copula Copula. GDP. Gaussian Factor Copula. 4-1. Gaussian Factor Copula. Step.1. 19.
(29) i. j. j. Step.2. Step.3. Factor Copula. Copula. Copula. 4.1. (Pearson). 20.
(30) Copula. Copula. Factor Copula Factor Copula. Copula Factor Copula. Copula. Factor Copula. Copula. 21.
(31) Chapter 5 5.1 LB BAVEN-WUERTTEMBERG. Gaussian Factor Copula. Copula. Bloomberg 5-1. 22.
(32) 2.. 3.. 5.2 Bloomberg 18. 5-2 5-2. MSCI MSCI MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI. MSCI MSCI MSCI 5-3 70% 79.97% 18. 90.85%. 23.
(33) 5-3. Factor=3. 70.69%. Factor=5. 79.97%. Factor=10. 90.85%. + +. +. 5.3 3.5 CDS. 40%. 5-4. 5-5. 5-4. 5-6. 2011Q1. -2.4091% -2.2929%. 5-1. 5-4. 2011Q3 CDS Spread. 24.
(34) 5-4. 25.
(35) 5-5. Copula. 26.
(36) 5-6. Factor Copula. 27.
(37) 5.4. 5-7. In-Sample. 5-7. 5-8 Copula. 28. Factor.
(38) Copula. Copula Factor Copula. 5-1. 5-2. Copula. Out-The-Sample. 5-8. Out-The-Sample. 29. Factor Copula. In-Sample.
(39) 5-1. 5-2. In-Sample. Out-The-Sample 30.
(40) (RMSE) n. i. RMSE. 5-9 In-Sample. Out-The-Sample. Factor Copula. 5-10. Copula Factor. Copula. Copula. Copula. Factor Copula Factor Copula. 3.1415 0.0393. 5-9. In-Sample In-Sample. RMSE. Factor = 3. Factor = 5. Factor = 10. Factor Copula. 3.1415. 3.1594. 3.1022. Copula. 3.9840 5-10. RMSE Factor Copula. Out-The-Sample. Out-The-Sample Factor = 3 Factor = 5 4.0295. 4.0306. Copula. 4.8078 31. Factor = 10 4.0028.
(41) Chapter 6 6.1. CDS. Copula. CDS. Factor Copula. Factor Copula. Factor Copula. 1.. 2.. Copula. Factor Copula. Copula. Factor 32.
(42) Copula. 3.. Factor Copula Copula. Copula 4.. 3.1415 0.0393. 33.
(43) 6.2. 1. MSCI. 2.. Jump. jump. 3. 40%. 34.
(44) [1]. Factor Copula 102. [2]. -94. [3]. CDO 97. [4] 93 [5] 94 [6] 91. 35.
(45) [1] GREGORY,. Jon;. LAURENT,. Jean-Paul.. In. the. core. of. correlation. RISK-LONDON-RISK MAGAZINE LIMITED-, 2004, 17: 87-91 [2] HULL, John C.; WHITE, Alan D. Valuation of a CDO and an n-th to default CDS without Monte Carlo simulation. The Journal of Derivatives, 2004, 12.2: 8-23. [3] LEE, Yu-Sung. Pricing Counterparty Credit Risk for Synthetic CDO Tranches. 2011, 1-31. [4] WU, Po-Cheng. Applying a factor copula to value basket credit linked notes with issuer default risk. Finance Research Letters, 2010, 7.3: 178-183. [5] RATHGEBER, Andreas; WANG, Yun. Market Pricing of Credit Linked Notes: The Case of Retail Structured Products in Germany. In: Annual Meeting Paper. EFMA. 2010. [6] BURTSCHELL, Xavier; GREGORY, Jon; LAURENT, Jean-Paul. A comparative analysis of CDO pricing models. 2005.. 36.
(46) Factor Copula. n. 37.
(47) 38.
(48) 39.
(49) 40.
(50) A.. =. B.. 41.
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