以傅立葉轉換評價債權擔保憑證

Abstract

在做擔保債權憑證的定價時，資產間的相關性是一個不容易處理的問題。資產總損失的分配是由一個很多維的聯合機率分配來決定，但是因為太過於複雜，因此有計算上的困難。本文延伸了前人的文獻，利用兩個主要的元素來解決這個問題：分別是因素模型以及傅立葉轉換，以期能夠達到快速的計算出擔保債權憑證個各分券的合理價格。

In pricing CDOs, the correlation between assets is a major issue. A multi-asset joint distribution function is too complicated to transform to a loss distribution. Chen and Zang developed a method to price a large credit portfolio. This method is composed of two elements: Factor model and Fourier inversion. This thesis generalizes their method. We assume that there are two common factors, and all assets have their own correlations with the common factors. Since the assets in a pool are not affected by only one common factor, and each asset has different degrees of influence over that common factor, we generalize the one-factor model with more accurate performance.