利用感染模型評價可擔保債權憑證

Abstract

市場上有許多評價可擔保債權憑證(CDO)的方法，其中最為市場廣泛接受的為穆迪評等公司的二項擴散理論(Binomial Expansion Theorem)。對於CDO的投資者來說，他們所承擔的不只是單一債券的違約風險，影響損失分配的因數還包含了債券回覆率與違約相關性。穆迪評等公司製造一個包含分散分數”D”個獨立債券相對應的資產池，利用二項分配理論模擬原有資產集合的違約情形。分散分數處理違約相關性的好處是分析簡單，但它不是模擬真正的違約情形。本研究介紹Davis and Lo的感染模型(Infectious Model)去解釋CDO資產的違約狀況，比較與穆迪分散分數的不同之處。我們對於不同分散分數與感染參數的投資組合，模擬其損失分配。研究發現隨著感染參數數值的增加，損失分配的變異數及尾端機率也跟著增加，這與分散分數的損失分配具有一致的情況。感染模型利用感染參數處理違約相關性，不必製造一個相對應資產池，而模擬資產真正的違約情形，它不但保留了BET模型的簡單性，還彌補了分散分數的不足。

There are many methods to price Collateralized Debt Obligation (CDO). One of the most well-known models for rating CDO is Moody’s binomial expansion technique (BET). Rating CDO does not only require attributing a probability of default to each obligor within the portfolio. It also involves assumptions concerning recovery rates and correlated defaults of pool assets. Moody’s analyze the credit risk by creating a reference portfolio which consists of D’s independent assets, then applies binomial distribution to simulate default events of the reference portfolio. The advantage of using diversity score is that it is easy to analyze but yet not simulate the actual default events. In this paper, we introduce the infectious model by Davis and Lo to explain the default events of the collateral, then we compare the difference with the diversity score. We simulate the loss distribution by different diversity score and infectious parameter. The bigger the infectious parameter, the bigger the variance and the tail-probability of the loss distribution would be. This is the same as the diversity score. Infectious model uses infectious parameter to deal with the default correlation without creating a reference portfolio. It simulates actual default events; not only does maintain the simplicity of BET but also addresses the shortcomings of the diversity score.