擔保債權憑證之評價－－Copula函數的應用

ON THE PRICING OF COLLATERALIZED DEBT OBLIGATION A COPULA FUNCTION APPROACH

本文的主要目的是透過市場上公開的資訊，建立一套擔保債權憑證之評價模型。在模型建構上，我們是以KMV模型將資產市價與違約風險做連結，估算出個別債務人的違約機率，並利用copula函數來描述擔保債權群組間的違約相關性。最後，在風險中立的假設下建構一套完整的架構以對擔保債權憑證之批次證券進行公平溢酬之定價。研究結果發現擔保債權憑證之風險溢酬受到許多因素所影響：若擔保債權群組之信用等級愈差、或相關性愈高、或回復率愈低、或批次證券之等級愈差、或損失臨界點愈低等均會造成風險溢酬的提高。由於此結果相當符合財務理論之要求，故我們認為在目前國內的違約資料庫不完備的情況下，本文可以提供實務界一個可行的擔保債權憑證之評價方法。

The purpose of paper is to develop a model to price collateralized debt obligations by using available market data. We use a KMV model to link the asset market price and default risk. In addition, we construct a copula function to describe the dependent structure of a collateral portfolio. Under the risk neutral measure, we can obtain the fair premium of different tranches of collateralized debt obligations. The simulation results show that the credit rating, dependent structure and recovery rate of collateral portfolio are important factors affecting the fair premium of different tranches. The ranking and loss of tranches are also important factors for the fair premium. This paper thus provides a useful pricing method for collateralized debt obligations, given the lack of a complete default database in Taiwan.