以BET、CBET及Copula方法評等現金流量型擔保債權憑證之比較

Abstract

擔保債權憑證(Collateralized Debt Obligations, CDOs)自1980年代首次出現於美國後，近三十年間發展十分迅速，用以計算各分券信用評等之模型五花八門，本文之目的即為了解目前三大評等機構，包含Moody’s發展之Binomial Expansion Technique(BET)及S&P和Fitch所採用的Copula是否存在有評等上之差異。 本文首先介紹CDO於美國與臺灣之發展歷史及其優點，詳述CDO之基本架構，包含其參與者、分類方式及資產群組現金流量分配方式(Waterfall)；接著介紹BET及Copula方法發展之歷史、評等架構及參數估計方式；最後以Markit所編制之CDX NA IG Series 9當中之公司作為樣本，建構一現金流量型CDO，並使用BET、CBET及Copula方法分別進行評等並比較其差異。 根據本文實證顯示，Copula方法所模擬之高等級分券預期損失較另兩種方法為高；反之，其低等級分券預期損失較低，可見資產違約相關性在Copula方法中之影響力相較於其在BET及CBET方法中之影響力來得強。此外，當資產違約機率向上變動時，BET及CBET之信用評等下降幅度較Copula大，特別是位於中間之B、C分券，顯示其對於資產違約機率之敏感性較Copula為高。

Since Collateralized Debt Obligations (CDOs) was invented in 1980s, there were many models developed in order to decide its tranche rating. The main objective of this paper is to find out if there are any rating differences between Moody’s Binomial Expansion Technique (BET) and Copulas adopted by S&P and Fitch. This paper begins with a brief introduction of how CDOs market was developed and advantages of CDOs. We describe the basic structure of CDOs including participants, classification, and waterfall. We also introduce the rating procedure of BET, CBET (Correlated Binomial Expansion Technique), and Copulas. Based on our study, Copulas tend to give higher expected loss to higher-grade tranches than BET and CBET, which means the default correlation plays a more important role in copulas than in BET and CBET. Besides, When default probability goes up, there would be a bigger impact on the credit rating given by BET and CBET than Copulas. This phenomenon shows that their sensitivities to default probability change are higher.