結合跳躍擴散槓桿比與 Hull-White 利率模型之可違約資產評價模型

Abstract

既有文獻對於信用衍生性金融商品之結構式定價模型發展，有其限制所在。本研究故此提出一模型，解決現有之結構式模型缺陷，以利於計算諸多可按標的公司資產負債水準計價之信用衍生性金融商品價格。 至於本模型之發展乃依據 Collin-Dufresne and Goldstein（2001）之研究，以對數槓桿比隨機過程為主架構，再搭配 Hull-White 隨機利率模型建構一立體樹狀模型。其後，更參考 Amin（1993）之研究方法，令樹狀發展進行跳躍擴散成長並對各分支落點做機率估計，以完成模型之金融商品定價回溯推算。 全文內容主要以模型樹狀之建構為主，其中包含前人文獻之細節回顧與數理計算推演過程等。次之，則以模型之定價為搭配，作為應用此模型之範例介紹。最後附上數值結果以供應證，並分析其可能之經濟意涵。

Researches on the structural pricing model are popular in decades. However, there are some restrictions in existed publishes. For the purpose of solving these problems, my study proposes a new model to calculate the price of the credit derivatives relating to the leverage of the firm. According to the paper of Collin-Dufresne and Goldstein ( 2001 ), my study used the process of the leverage of the firm to be the framework of my model. I also considered the stochastic interest rate process by combining Hull-White model with the process of the leverage to be a three-dimensional tree model. Furthermore, I added the jump diffusion process with the probability according to Amin ( 1993 ) to complete my model. Finally, my research used the backward induction to compute the price of the credit derivatives, such as corporate bond and credit default swap spread.