Pricing Portfolio Credit Derivatives Using a Simplified Dynamic Model

本論文主要是在介紹評價信用衍生性金融商品的動態模型，並應用之來評價標準化的擔保債權憑證（CDO）商品，iTraxx Europe index。此動態模型相對於之前市場上常用的copula靜態模型，應用的範圍更廣，其可以評價更多的新奇型信用衍生性商品。本文引用了Hull and White (2007)提出的簡單動態模型的概念，修改其中幾項模型參數並探討出較合適的評價過程，使此模型更具經濟上的意義。除了直接的解析解，我們還探討了二元樹與蒙地卡羅模擬的方法，使評價過程更具多元性。其中我們補足了此模型轉成二元樹模型的數學證明，使此模型的架構更加完整。最後，我們發現此模型帶入市場資料後所求得的商品分券價值亦相當接近於市場價值。This thesis investigates dynamic methods for pricing portfolio credit derivatives, especially the standardized market for CDO: iTraxx Europe index. Compared with previous static models, i.e., the copula functions, the dynamic models are applicable to much more exotic portfolio credit derivatives. This thesis uses the concept of the dynamic model from Hull and White (2007). But we modify it by adjusting some parameters. We also find a better way for calibration to give the model more economic sense. The iTraxx Europe index can also be valued analytically using our model. Besides the analytic method, we consider the binomial tree and Monte Carlo method to make pricing more flexible. Finally, the revised dynamic model captures the advantages of the original one and also provides a good fit to CDO quotes.1. Introduction 1.1 Background and Literature Review 1.2 Structures of the Thesis 2. A Primer on CDO and Index Tranche Pricing 3.1 Introduction to an Index Tranche 3.2 Extract Implied Default Probability from CDS Spread 4.3 Valuation of a CDO 5. The Dynamic Model and Its Implementations 7.1 The Dynamic Model 7.1.1 Model Review 7.1.2 Model Modification 8.2 Three Implementations of the Model 8.2.1 Analytical Method 8.2.2 Binomial Tree Method 9.2.3 Monte Carlo Simulation Method 12. Calibration and Numerical Results 13. Conclusion and Future Work 20. Poisson Process 21. Expectation of Hazard Rate 23ibliography 2