隨機回復率架構下之擔保債權憑證評價模型比較

Abstract

2007年起，由於次級房貸事件爆發，以及接踵而至之信用危機及經濟衰退，使許多信用衍生性商品之信用利差大幅攀升，造成在標準市場模型（One Factor Gaussian Copula）的架構下無法求取Base Correlation，特別是CDX.NA.OG [15, 30%]以及iTraxx Europe [12, 22%]兩優先批次證券。Base Correlation為市場參與者在計算避險係數和結算損益之重要參數，若無法求取將不利於信用衍生性商品之流動性。 Amraoui and Hitier （2008）提出改變回復率之做法來改善標準市場模型，在One Factor Gaussian Copula模型中，將回復率（Recovery Rate）由原本固定常數改成為系統因子之一函數，隨系統因子之水準不同而改變，而Amraoui and Hitier發現改進後的模型能夠降低Base Correlation之水準，並且減少Negative Delta之現象。目前Amraoui and Hitier模型廣為實務上所接受使用，唯仍然建立於Gaussian分配之架構下。本篇論文建立於Amraoui and Hitier對回復率之假設，以Student t分配來取代原本Gaussian分配，試圖建立一擔保抵押債權之評價模型，來和Amraoui and Hitier模型比較其優劣。在本論文中，首先求算不同模型在參數改變下之評價結果，來探討不同評價模型之特性，接著以Base Correlation及Correlation Skew兩個面相來比較不同模型，進而尋求更完整且實用之信用衍生性商品評價模型。

Since mid-2007, the outburst of subprime crisis and the consecutive credit crunch as well as economic recession have led to the recent widening in super-senior spreads, which pushed the base correlation to its limits that can be allowed under One Factor Gaussian Copula (OFGC) model. Base correlation is mainly used by market practitioners in calculating hedge ratio, mark-to-market profit and loss and the spreads of bespoke tranches. Hence, the inability to calibrate base correlation could have seriously negative impact on credit market. Amraoui and Hitier (2008) proposed a new method to enhance OFGC model by modeling the recovery rate as a deterministic function of the systematic risk. The new model can reduce the levels of base correlation for each tranches and the number of negative deltas for super senior tranche (ex: CDX.NA.IG 15-30% tranche), yet it has been built under the framework of Gaussian distribution. In this paper, we replace Gaussian distribution with Student-t distribution under the stochastic recovery rate model proposed by Amraoui and Hitier (2008). In our study, we look into the parameter sensitivities of the two models and then compare the two models in terms of the results of pricing and base correlation.