# 臺灣博碩士論文加值系統

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 本文針對債券投資人所關切的信用風險，將 copula 函數加入既有測量信用風險值的 CreditMetric 模型，以考量資產間複雜的相依結構，據此提供債券投資人評估信用風險值 (credit VaR) 的參考依據。依據債券發行公司間的資產相依結構 (dependence structure) 以及 Standard & Poor’s 發佈的信用評等移轉矩陣 (credit transition matrix)，計算此投資組合於年終移轉至各個信用評等的預期價值與其對應的機率分佈圖，以估算此投資組合的信用風險值。不同於傳統常態分配的設定方法，本文利用 Archimedean copula family (以下簡稱 AC copula family) 來描述公司資產間複雜的相依程度。並依據 Genest and Rivest (1993) 所提出的無母數估計方法，估計美國上市公司所發行公司債投資組合的信用風險值。本文發現，整體來說公司間的資產相依結構並非如傳統常態分配所設定的模型一樣，而是具有厚尾 (fat tail) 的情況產生。並且針對投資者所關心的尾端風險，相較於Kendall’s tau等級相關係數則lower tail dependence更能描繪資產組合尾端的變化狀態，以幫助本文更精確且進一步的評估投資組合的信用風險值。
 In this thesis, our aim was establish a framework as CreditMetrics for quantifying credit risk in portfolios of corporate bonds. We depended on assets dependence structures of corporate bonds and Standard & Poor’s credit transition matrices to compute all possible 64 year-end values and all possible 64 year-end joint likelihoods across 64 different states for a two-bond portfolio. The next step was to assessed the credit value-at-risk (Credit VaR).In this thesis, we focued on the problem of modeling the multivariate distributions of several outcomes. To solve this problem we used a promising approach based on Archimedean copulas which is different from the conventional multivariate Normal assumption to focus explicitly on the dependence structure. We used the nonparametric methods of Genest and Rivest to assess the credit value-at-risk for American corporate bond portfolios. Our empirical distributions were heavier tailed than the normal distribution. If investors ignore this phenomenon, they will underestimate the VaR and make a downside loss.
 1. Alsina, C., M Frank,. and B. Schweizer, 1998, Associative Functions on Intervals, in preparation.2. Black, F. and M. Scholes 1973, The pricing of options and corporate liabilities. Journal of Political EcoNomy, 81, No3, 637-653.3. Bouyé E, V. Duttlrmsn, A. Nikeghbali, G. Riboulet et T. Roncalli 2000, Copulas for finance: a reading guide and some applications, working paper.4. Claudio, C. 2002, Applying copula function to risk management, working paper.5. Coyle, B. 2000, Measuring credit risk, NY: AMACOM.6. Credit Swiss First Boston products 1997, Credit Risk+ - Technical Document, Landon/New York.7. Embrechts, P., A. McNeil, and D. Straumann 1999, correlation and dependence in risk management properties and pirfalls, To appear in Risk Management: Value at risk and Beyond, ed. By M. Dempster and H.K. Moffatt, Cambridge University Press.8. Embrechts, P., F. Lindskog, and A. McNeil 2001, Modeling dependence with copulas and applications to risk management, working paper.9. Fama, E. F. 1965, The Behivior of Stock Market Prices, Journal of Businesss, 38, 34-105.10. Genest, C. and J. McKay, 1986, The joy of copulas: Bivariate distributions with uniform marginals, Amer. Statist. 40, 280-285.11. Genest, C. L. and Rivest, 1993, Statistical inference procedures for bivariate Archimedean copulas, Journal of the American Statistical Association, 88(423): 1034-1043.12. Guption, G. M. 1997, The new talk of town: CreditMetricsTM , a credit value at risk approach, Journal of lending & Credit risk Management , August, 44-54.13. J.P. Morgan products 1997, CreditMetrics™ - Technical Document, New York.14. KMV products 1995, Measuring and Managing Credit Risk: understanding the EDF - Technical Document Credit Measure for Public Firms.15. Li, D. X. 2000, On default correlation：a copula function approach, working paper, 1-7.16. Mandelbrot, B. 1963, The Variation of Certain Speculative Prices, Journal of Business, 36, 394-419.17. McCulloch, J. H. 1975, The Tax-Adjusted Yield Curve, Journal of Finance, 30, 811-830.18. McKinsey Consulting products 1998, CreditPortfolioView, Approach Documentation and User’s Documentation.19. Merton, R. 1974, On the pricing of corporate debt：the risk structure of interest rates, Journal of Finance 29, 449-470.20. Nelson, R. 1998, An Introduction to Copulas, Springer, New York.21. Qin, J. and B. Zhang, 1997, A goodness-of-fit test for logistic regression models based on case-control data. Biometrika. 84, 609-18.22. RiskMetrics Group products 2001, RiskGrades: Technical Document, New York.23. RiskMetrics Group products 2002, CreditGrades - Technical Document.24. Schweizer, B. and E. Wolff, 1981, On nonparametric measures of dependence for random variables, Ann. Statist. 9, 870-885.25. Sklar, A. 1959, Functions de répartition à n dimensions et leurs marges, Publications de Inst. Statist. Univ. Paris 8, 229-231.26. Wang, K. C. Fawson, and J. Barrett, 2000, An Exchange Rate Application of GARCH-EGB2 Models, forthcoming by Journal of Applied Econometrics.
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