以Merton模型評價擔保債權憑證-簡易法

本文採用Bharath and Shumway (2008)衡量Merton模型變數的研究方法模擬債權群組的違約機率，以規避傳統Merton模型變數之非線性方程式求解過程。並且以Copula函數估計債權群組之間的違約相關性，進而推導出擔保債權憑證(CDO)之公平信用價差。本文參照Gibson(2004)衡量分券風險的指標，分析擔保債權憑證各個分券之損失乘數。模擬各個分券之結果顯示，已實現損失雖對權益分券造成損害，卻同時降低違約損失的不確定性，因此權益分券的損失槓桿倍數對存續期間之敏感度呈現遞減；反觀次級、先償順位分券，期初投入的本金所受到的保護層縮水，對違約事件的敏感程度相對提高，其損失槓桿倍數隨時間經過而上升。最後，本文發現以Bharath and Shumway(2008)方法所求算之非預期損失率對預期損失率的增加幅度相對於原始Merton模型低，顯示較能捕捉極端違約事件，對已實現損失的衡量精確度相對提高。

關鍵字

擔保債權憑證； Merton模型； Copula函數；傳染效應；槓桿倍數

並列摘要

This article we investigate the valuation and risk management issues of collateralized debt obli¬gations (CDO). We use the naïve approach proposed by Bharath and Shumway (2008) to avoid simultaneously solving the two nonlinear equations. And we construct Copula functions to describe the dependent structure because the contagion effect of collateral pool has an important impact on fair premium of differ¬ent tranches. The risk of CDO tranches can be measured in various ways, and we present two risk measures by Gibson (2004). The simulated results show that the equity tranche has relatively more risk than others and the uncertainty of realized loss would become insensitive to the maturity of CDOs. On the contrary, the protected levels of the senior tranche would be gradually weak, thus its leverage numbers become more sensitive. Fi¬nally, in comparison with Merton model, we find that the increasing amount of unexpected loss relative to ex¬pected loss computed by the naïve alternative model significantly declines, so this implies that the accuracy of estimated realized loss increases. We conclude that the undervalued default probabilities would be improved by the naïve alternative model; that is, predicting the default events of CDO becomes more accurate.