評價信用衍生性商品之動態違約系統的模型建構

Pricing Portfolio Credit Derivatives Using a Simplified Dynamic Model

林冠志(Kuan-Chi Lin)

指導教授 ： 呂育道

國立臺灣大學/管理學院/財務金融學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.01929

摘要

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。

關鍵字

信用衍生性金融商品 ； 擔保債權憑證 ； 動態模型

並列摘要

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.

並列關鍵字

portfolio credit derivatives ； iTraxx Europe index ； dynamic model

參考文獻

Brigo, D. and F. Mercurio, 2007, Interest Rate Models — Theory and Practice: With Smile, Inflation and Credit, Berlin, Springer.

Brigo, D., A. Pallavicini and R. Torresetti, 2007, “Calibration of CDO Tranches with the Dynamical Generalized-Poisson Loss Model,” Risk 20, May, 70–75.

Graziano, G. and L.C.G. Rogers, 2006, “A Dynamic Approach to the Modeling of Correlation Credit Derivatives Using Markov Chains,” Working paper, University of Cambridge.

Gregory, J. and J.-P. Laurent, 2005, “Basket Default Swaps, CDO’s, and Factor Copulas,” Journal of Risk 7, 8–23.

Hull, J., 2006, Options, Futures, and Other Derivatives, 6th ed., Englewood Cliffs, Prentice-Hall.