考慮隨機回復率與額外違約風險下合成型擔保債權憑證之評價

Synthetic CDO Pricing with External Default Risk and Random Recovery

蔡奇錚(Chi-Cheng Tsai)

指導教授 ： 鍾麗英

國立臺北大學/商學院/統計學系/碩士(2009年)

摘要

信用衍生性商品在近幾年來急速發展，而該商品價格的決定是一重要議題，其中對合成型擔保債權憑證 (synthetic CDO) 之評價更是許多文獻主要研究的方向。而 Gaussian Copula 模型因其簡單及便利性成為市場上標準的評價模型，但這模型存在著一些問題，一是常態分配不具有肥尾現象，這並不符合市場上的狀況，二是模型中假設回復率、違約強度、資產相關係數等參數為一常數，但我們知道這並不合理，這些參數皆會隨著市場上的情況不同而改變，三是快速違約事件會造成存活下來的公司的違約機率迅速升高。因此，本篇利用 T 分配及 Normal Inverse Gaussian 分配去改善常態分配不具有肥尾的問題，接著，我們考慮隨機回復率，打破回復率為一常數的假設並且使用額外違約模型去解決第三個問題。最後，我們會用我們的模型去對市場上標準的合成型擔保債權憑證─DJ iTraxx EUR 及 DJ CDX.IG 做評價，我們發現使用 T 分配及 Normal Inverse Gaussian 分配的評價結果會比使用 Gaussian 分配來的好，而且考慮隨機回復率具有微調的效果。另外，額外違約模型的表現會隨著市場情況不同而改變。當景氣不好時，額外違約模型有比較好的評價結果，而另一方面，我們發現我們校準出來的參數很接近市場上的情況。因此，當考慮厚尾分配、隨機回復率與額外違約模型會改善我們的評價結果。

關鍵字

合成型擔保債權憑證 ； Copula 模型 ； 隨機回復率 ； 額外違約模型

並列摘要

Collateralized debt obligation (CDO) develops very fast in recent year; the price of this product is an important issue. The major research of past literatures investigated that how to price the synthetic CDO. One factor Gaussian copula model becomes the standard pricing model because of its simplicity, but this model exists some problems. First, the Gaussian distribution doesn’t have fat-tailed; this phenomenon doesn’t coincide with the market state. Second, pairwise correlations, default intensities and recovery rates will not equal and constant for all assets in the reference portfolio and different market situations. Third, the impact of fast default event will cause the default probabilities of survivors become higher. Hence, we use fat-tailed distribution – Student t and Normal Inverse Gaussian distribution – to solve first problem. Then, we consider random recovery to release the assumption of recovery rate is constant, and using external default model to solve last problem. Final, we will utilize our model to price DJ iTraxx EUR and DJ CDX.IG. We find that using fat-tailed distirbutions the pricing results will more precise than Gaussian distribution, and considering random recovery has little adjusted effect. The performances of external default model are different according to market sutiautions. When the market is in bad time, the external default model has better behavior. On the other hand, we find that the calibrated parameters are close to market situations. Therefore, when taking account of fat-tailed distributions、random recovery and external default model will improve our pricing result.

並列關鍵字

sythetic CDO ； Copula model ； random recovery ； external default model

參考文獻

1. Altman, E. I., Brady, B., Resti, A., & Sironi, A. (2005). The link between defaultand recovery rates: Theory, empirical evidences, and implications. Journal of Business, Vol. 78, No. 6 , pp. 2203–2227.

2. Amraoui, S., & Hitier, S. (2008, June). Optimal Stochastic Recovery for Base Correlation. www.DefaultRisk.com .

3. Andersen, L., & Sidenius, J. (2004 winter). Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings. Journal of Credit Risk, Vol. 1 , pp. 29-71.

5. Chourdakis, K. (2008, March). The Cyclical Behavior of Default and Recovery Rates. www.DefaultRisk.com .

6. Ech-Chatbi, C. (2008, September 17). CDS and CDO Pricing with Stochastic Recovery. www.DefaultRisk.com .