跳躍過程與隨機利率下之信用違約交換訂價模型

Abstract

本篇論文提出在資產價值滿足跳躍擴散過程且無風險利率為CIR架構下的信用違約交換契約的評價模型。並提出在此一模型假設下如何利用拉普拉斯轉換及逆轉換求得違約機率及信用違約交換價差的近似解。同時，本研究亦比較了跳躍擴散過程及傳統擴散過程對違約機率及信用違約交換價差所造成的影響。 在模型驗證方面，本文使用美國S&P500其中四十三個公司資訊來進行分析，並同時比較了在跳躍擴散過程與傳統擴散過程下信用違約交換契約之訂價誤差。本研究發現當資產滿足跳躍擴散過程時，訂價誤差遠比傳統擴散過程來的小。

This thesis suggests that asset value satisfies jump-diffusion process and that risk-free rate follows CIR process is the CDS assessment model. It also points out the way to obtain the approximate formula to the probability of default and CDS spread from the Laplace transform and the inverse of Laplace transform. Meanwhile, this research compares the effects that the jump-diffusion process and diffusion process have on the probability of default and CDS spread. As for the test of the model, this thesis analyzes the data based on forty-three companies out of American S&P500. It compares the pricing error of CDS under the jump-diffusion and diffusion process. The study shows that as the assets value satisfy the jump-diffusion process, the pricing error is far less than diffusion process.