結合可違約股價樹與Hull-White利率樹之CDO評價模型

Abstract

擔保債權憑證(Collateralized Debt Obligation, CDO)的評價，無論是採用採用結構型模型(Structural Model)或縮減式模型(Reduced Form Model)都有評價上的困難而無法準確評價。同時由於CDO是固定收益商品的一種，因此在評價時也該考慮利率的變動的影響。Bandreddi, Das, and Fan (2007)提出的二元樹CDO評價模型兼具結構型模型與縮減式模型的優點，但樹上的分枝機率可能為負數，而且此模型也未考慮利率的隨機過程。本篇論文採用該模型的架構，並加以延伸改良。首先，我引進了Dai (2009)所提出的mean-tracking演算法以解決利率可能為負數的問題。接著，我將Hull and White (1994)所提出的利率樹模型與上述的股價樹模型結合。之後再修改違約強度函數，使其能衡量利率的影響以及更準確的配適駝峰狀的違約期限結構。最後本研究也將用此模型評價iTraxx CDS指數以作為簡單的實證測試，並分析本模型的評價結果。研究結果顯示mean-tracking演算法能有效的提升評價的準確度，但加入利率過程及修改違約強度函數的效果卻不夠顯著。另外本研究的評價結果也會隨著違約相關係數的不同而敏感地變動，這說明了在CDO的評價模型中，違約相關係數是最重要的參數。

It is difficult to price CDOs no matter using the structural model or the reduced form model. Moreover, since the CDOs are fixed-income security, it is intuitive to consider the process of interest rates. In this article, I extend the defaultable tree model proposed by Bandreddi, Das, and Fan (2007) to price CDOs. Their model provides both the good property of structural model and reduced form model but is probable to have the negative probabilities in branching and does not consider the interest rate process. First, I implement the mean-tracking algorithm introduced in Dai (2009) to solve the problems of negative probabilities in the defaultable stock tree model. In addition, I combine the stock tree with the interest rate tree proposed by Hull and White (1994) to implement the interest rate process. Furthermore, I revise the default intensity function to consider the impact of interest rate. Finally, my model is applied to pricing iTraxx as a simple empirical study. The result shows that the using of mean-tracking algorithm would improve the accuracy of pricing significantly. Moreover, the most important factor in pricing CDOs is the default correlation since my pricing results vary with the level of default correlation sensitively.