動態投資組合信用風險模型及出生過程

Abstract

本篇論文希望能夠提供一個簡潔並且Analytical Tractable的動態模型，做為於傳統靜態的Gaussian Copula模型之外另一個吸引人的選擇。在我們的模型當中，違約強度(Default Intensity)受到一個Deterministic的Drift和一個Impulse的影響，Impulse發生服從一個出生過程，而高度(Size)則會逐漸增強，這個總體經濟情況產生的Impulse就扮演著Gaussian Copula Function中Correlation的角色。這個模型不僅僅可以準確符合CDS的結構(Term Structure of CDS)，並且可以用於評價在不同到期日(Maturity)的CDO批次證券。而我們的模型更具有傳統Gaussian Copula Approach所沒有的經濟意含：就是隨著大環境的演變，當經濟體情況惡劣時，投資組合內公司違約的情形會更為的嚴重，違約的相關性也更高。而這樣的一個動態投資組合信用風險模型能夠讓提供我們一個直接並且Analytical Tractable的方法評價其他的信用衍生商品，例如Forward CDOs。

We wish to provide a both simple and analytically tractable dynamic model of portfolio credit risk, as an attractive alternative model of traditional Gaussian Copula model. In our model, the default intensity is governed by a deterministic drift and an impulse, where the impulse follows a pure birth process and the impulse intensity will increase from time to time. This impulse caused by the macroeconomics phenomena plays a similar role of the correlation factors of Gaussian Copula model. This dynamic model could not only accurately fit the term structure of the CDS spread but also is useful in the valuation of CDO tranche spreads of different maturities. Furthermore, our model include more economical sense and empirical phenomena than traditional Gaussian Copula approach; for example, as the default environment worsen, the default probability of the companies of the portfolio increase, and the default correlation rise as well. Finally, this dynamic model of portfolio credit risk will provide us a straight forward and analytical tractable way to value other portfolio credit derivatives, such as forward CDOs.