二次擔保債權憑證損失率敏感性分析: 以外層夾層分券為例

Abstract

本文主要藉由逐次改變二次擔保債權憑證的內層分券金額佔資產池發行金額比例、內層分券下層信用保護金額佔資產池金額比例、資產池參考標的間違約相關性、到期期限、及違約回收率等五項影響二次擔保債權憑證損失發生機率的風險因子，結合蒙地卡羅模擬法及關聯結構法模擬交易架構中內層、外層分券不同損失率的發生機率，並利用彈性分析，衡量二次擔保債券憑證在每單位風險因子變動下，內層及外層分券的損失發生機率。\r\n 研究結果顯示，相同的風險因子對於內層與外層分券的損失發生機率的影響效果並不相同，此一現象有別於一般認為風險因子對內、外層分券損失發生機率影響效果相同的看法。此外，依據分券損失發生機率對每單位風險因子變化的彈性敏感性分析，分券損失發生機率受風險因子的影響可分為: 彈性為正且數值逐漸增加、彈性為正且逐漸下降、彈性為負且數值 (絕對值) 逐漸下降、及彈性為負且數值 (絕對值) 逐漸增加四類。外層夾層分券的損失發生機率對內層分券厚度占資產池金額比例的彈性為負，其數值 (絕對值) 隨著內層分券厚度占資產池金額比例的增加而下降。外層夾層分券的損失發生機率對內層分券下層信用保護金額佔資產池金額比例的彈性、及外層夾層分券的損失發生機率對參考標的違約回收率的彈性為負，且數值 (絕對值) 隨著下層信用保護比例及回收率的增加而上升。外層夾層分券的損失發生機率對參考標的違約相關係數的彈性為正，其數值隨著相關係數的增加而下降；外層夾層分券的損失發生機率對參考標的之到期期限的彈性為正，其數值隨著到期期限的增加而上升。

The researchers of this study combined Monte Carlo simulation approach and copula method to change the following five risk factors: the thickness of inner CDOs tranche on CDO-squared, the subordination in master CDOs tranche, the correlation of reference entities, the maturity of reference entities, and the recovery rate of reference entities, with a purpose of simulating the loss possibility of CDOs-squared. Besides, by elasticity analysis, the researchers measured the change of loss rate according to the change of each risk factor per unit.\r\n The result of the study shows that the same risk factor has different influence on the loss rate of inner and master tranche of CDOs squared, which mismatches the general belief that the same risk factor has the same effect on the loss rate of inner and master CDOs tranche. In addition, according to the tranche loss possibility elasticity analysis to the risk factors, this research reveals that four categories can be made due to the effect which risk factors have on loss rate : positive and increasing elasticity, positive and decreasing elasticity, negative and increasing elasticity, and negative decreasing elasticity. We found that for the master mezzanine tranche: the elasticity of tranche loss possibility to the thickness of inner CDOs tranche of CDO-squared is negative and will decrease with the increasing thickness of inner CDOs tranche. The elasticity of tranche loss possibility to subordination in inner CDOs tranche and the elasticity of tranche loss possibility to the recovery rate of reference entities are both negative and will increase with the increasing subordination of inner CDOs tranche and the recovery rate of reference entities. The elasticity of the loss rate possibilities to the correlation of reference entities default is positive and will decrease with the increasing correlation of reference entities. The elasticity of loss possibilities to the maturity of reference entities is positive and will increase with the increasing maturity.