結合D-CRR、多種GARCH及均值對稱方法評價CDOs

Abstract

本篇論文參考Lin (2010)可破產三元樹與Peter and Kris (2004)不同GARCH 模型之比較，已可破產三元樹在不同GARCH模型下對CDOs做評價，比較配合不同GARCH模型對CDOs評價結果何者最佳。Charles and Andrew (1987) parsimonious model之期間結構對不同型態的資料皆有良好的配適情形，因此我們以Charles and Andrew (1987) parsimonious model來調整破產強度公式。 實證部分，我們以股價校正GARCH參數，再以CDS資料校正破產強度參數，最後使用模擬方式估計CDOs各分券之價差，並與實際市場資料做比較，我們發現到期期間愈長則可縮小估計均方差，Simple GARCH process之模擬結果最佳，此結果與Peter and Kris(2004)之結論相符，以較簡約之GARCH模型作衍生性商品評價，其結果最佳。

Following the work of Lin (2010) and Peter (2004), we use the Defaultable Trinomial Trees under different GARCH Processes to value the spread of CDOs and compare the performances under different GARCH processes. Motivated by the success of Charles and Andrew (1987) parsimonious model, we modify the term structure of the default density function with parsimonious model. In empirical research, we calibrate the parameters with the stock prices and CDS spread and use Monte Carlo to estimate the spreads of iTraxx Europe Series 15. Comparing the estimators under different GARCH processes, we find that the estimators of 7-year CDOs spread are better than the estimators of 5-year CDOs spread. In addition, Simple GARCH process is better than other GARCH processes when valuing CDOs spread no matter with real correlation matrix or with constant correlation matrix. This result is correspond with Peter and Kris(2004).