The Analysis Of Some Pricing Models Under Credit Risk In Uncertainty

By the development of Credit Risk globalization, the control and management of Credit Risk attract more market participants's attention. Especially after the world-wide global financial crisis in 2008, let people realized the importance of the control of Credit Risk. In this paper, we introduce the theory of Uncertainty to study the quality of European option, and to analysis the default in some important model in Credit Risk.The theory of Uncertainty was presented by BaoDing Liu professor in Tsinghua University in 2007. The Uncertainty theory study the Uncertainty problem in real life. It included probability, credibility, chance, Uncertainty.This paper divided five part. The first part introduced the developments of Credit Risk and Uncertainty theory. The second part, in this paper, introduced and analysis detailedly the structural approach, reduced approach, and KMV model. The third part introduced the basic concepts and some important theorems. According to this basic concepts and theorems, we get the call-put parity of European options in Uncertainty,linear relationship of European call-put options, and a inequality about American call call-put options. After that, we introduced the fraction Liu process in credibility to Uncertainty, and get the expect and variance in fractional canonical process. By the definition of fractional canonical process, we can get the membership function about arithmetic fractional process and geometric fractional canonical process, also get the expect about geometric fractional canonical process. The fourth part, we used the knowledge of Uncertainty to analysis some model default which included Merton model,FPT model and KMV model, and get some useful conclusions. The fifth part gets some conclusions and respects.