擔保債權憑證評價：各種copula模式之比較

Abstract

對於擔保債權憑證的評價方法，目前最廣為接受的是Copula模式。一般認為Copula模式可對倒帳相關性有較適當的描述，且若與蒙地卡羅模擬法搭配，可以有效完成擔保債權憑證的評價。但Copula函數可有數種型式，到目前為止，尚無文獻試圖找出何種Copula函數是最適用的，本篇論文即是希望發展出一套方法來選擇最適的Copula函數。 本篇研究比較四種Copula函數（Gaussian, t, Clayton, Exponential copula），且以三個衡量構面來比較各Copula的差異：Simulation速度、Calibration便利性、及Tail Dependence構面。以往文獻只就Copula Function的Tail Dependence性質進行比較，並未對不同CDO之資產群組作深入分析。因此，本篇研究提出一套方法來將Tail Dependence應用至CDO商品上，使得此CDO最適Copula Function的尋找更為完善。

For the various approaches to CDO valuation, the most widely accepted is the Copula approach. The Copula approach is considered suitable for describing default correlation. Combining with Monte Carlo Simulation, it can price CDO effectively. However, several forms of copula functions have been proposed. And attempts to compare these functions based on different dimensions such as the speed of simulation, the ease of calibration, and tail dependence structure have been conducted. In this paper, we propose a way to extend the tail dependence as to take into account the asset structure of different CDOs. With the extension, the search of the most appropriate copula function will be more complete.