利用具相關性之二元樹模型做信用組合違約模擬

Abstract

本文中我們首先回顧Das and Sundaram (2004)與Bandreddi, et al. (2007)所提出的模型。Das and Sundaram (2004)提出了一個考量股價、利率、及信用風險的簡易二元樹模型，應用在可轉換債券之評價。Bandreddi, et al. (2007)利用該模型之簡化版來模擬具相關性的信用組合之違約行為。在我們的研究當中發現，於他們的模型設定之下會使得建立的二元樹上有不合理之風險中立機率值，而這些問題機率將使得模擬出的違約結果以及計算出之衍生性商品價格有偏誤。我們提出另一個模型，稱做D-CEV模型，用以替代原先之模型及解決該機率問題。該模型是傳統上考量股價槓桿效果（leverage effect）的二元樹模型之延伸，並且容易實作。我們更研究了我們所提出之模型的許多特性，發現我們的新模型不但能減緩Bandreddi, et al. (2007)之模型的許多缺陷，也能保留其良好屬性。我們更指出這樣的架構下如何滿足實證上能觀察到的許多現象，並且比較兩模型用以評價擔保債務憑證（Collateralized Debt Obligation）的結果。設定不同情境之下，Bandreddi, et al. (2007)之模型所評價出之價格皆低於我們提出之模型所得到的價格，且在不合理機率越多之下差異越顯著。

We revisit the models developed in Das and Sundaram (2004) and Bandreddi, et al. (2007). Bandreddi, et al. (2007) use a simplified version of the model developed by Das and Sundaram for correlated default simulation. We find that in their setting, problematic probabilities may arise which may cause biased results for the purpose of default simulation and the pricing of derivative products. We suggest an alternative model — the D-CEV model, as an alternative to address this problem. The new model is an extension of a popular binomial model and is easy to implement. We further explore the natural characteristics of our method with several numerical experiments. Our proposed model is found to resolve the unpleasant flaws in the model of Bandreddi, et al. (2007) while preserving its desirable properties. We also show how this framework accounts for several empirical features.