擔保債權憑證 (collateralized debt obligation, 簡稱 CDO) 的核心觀念為 : 透過正確評估 CDO 群組資產中個別債務人本身的違約機率, 及群組資產債務人間的違約相關性, 來有效控制整個 CDO 商品的績效與信用風險. 而本文主旨為透過妥善的債務人違約機率及違約相關性衡量下, 提供一完整的 CDO 信用風險批次 (tranche) 評價方式以供參考. 在本文中,我們使用歷史的公開市場財務報表及股價等資訊, 利用 KMV 模型推導出個別債務人的違約機率, 其結果相當程度地反應出債務人在該段時間之真實信用風險情況. 此外,本文亦利用了近來在財務領域上廣被應用的 copula 函數來描述債務人彼此間的違約相關性. 而在最後的實證探討上, 我們是依據 Laurent and Gregory (2003) 的 CDO 信用風險批次定價模型,利用台灣市場上具有明顯公司信用風險差異的兩組樣本,結合不同類型的 copula 函數及違約回復率,分別對此兩組樣本做定價模擬.從最後的 CDO 信用風險批次溢酬模擬結果中, 我們亦驗證了 CDO 信用風險批次價值將受到個別債務人違約機率, 違約相關性及違約回復率影響.

To evaluate the default probability and the default correlation are two important issues for pricing the collateralized debt obligation (CDO). In this paper, we
provide a complete pricing procedure for CDO tranches. First, we use a KMV model to construct the default probability of each obligor. We then apply copula functions, which are now widely used in financial research, to consdier the default correlation between obligors. For the empirical studey of Taiwan data, we employ a pricing model proposed by Laurent and Gregory (2003) to evaluate CDO
tranches. It can be seen that the credit risk premium of a CDO tranche would be affected by the default probability, the recovery rate and the default correlation between obligors. These empirical results are consistent with the general consensus.

1. 黃裕烈, 張淑芳, 張焯然 (2005), 擔保債權憑證之評價模式,未發表之論文.
2. Black, F. and M. Sholes (1973), The Pricing of Options and Corporate Liabilities,Journal of Political Economy, 81, 637–654.
3. Black, F. and J. Cox (1976), Valuing Corporate securities: Liabilities: Some Effects of
Bond Indenture Provisions, Journal of Finance, 31, 351–367.
4.Davis, M. and V. Lo (1999), Infectious Default, Research and Product Development, Tokyo - Mitsubishi International Plc, London.
5. Davide, M. and V.Walter (2003), Copula Sensitivity In Collateralized Debt Obligations and Basket Default Swaps, The Journal of Futures Markets, 24(1), 37–70.
6. Duffie, D. and N. Garleanu (2001), Risk and valuation of collateralized debt obligations, Finanical Analyst’s Journal, 57(1), 41–62.
7. Frey, R. and A. J. Mcneil (2001), Modeling dependent defaults. Zurich : ETH.
8. Goodman, L. S. (2002), Synthetic CDOs: An Introduction, The Journal of Derivatives, 57(1), 41–62.
9. Jarrow, R. A. D. Lando, F. Yu (2001), Default Risk and Diversification: Theory and Applications, Working paper, Cornell University.
10. Jeffrey, R. Bohn (1999), Using Marketing Data to Value Credit Risk Instruments, KMV corporation, 27-Sept.
11. Laurent, J. P. and J. Gregory (2003), Basket default swaps, CDO’s and factor copulas, Technical Report.
12. Li, D. X. (2000), On Default Correlation: A Copula Function Approach, Journal of Fixed Income, 9, 43–54.
13. Merton, R. (1974), On The Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Applied Corporate Finance, 29, 449–470.
14. Nelsen, R. B. (1999), An Introduction to Copulas, Lecture Notes in Statistics , Spring-Verlag, New York.
15. Sklar, A. (1959), Functions de repartition a n dimensions et leurs marges, Paris: Publ. Inst. Statist. Universite de Paris , 229–231. 39
16. Stefano, S. G. (2003), Copula Fuctions and Their Applicatin In Pricing and Risk Managing
Multiname Credit Derivative Products, London University.