随机利率下CDS动态价格的研究

发布时间：2018-07-04 22:17

本文选题：CDS + BSDE系统　；参考：《上海交通大学》2014年硕士论文

【摘要】：我们假定无违约风险的瞬时远期利率满足不带跳的HJM模型，引入正有界的F-可料的违约强度过程并介绍了域流扩张的相关结论。在上述假设条件下，我们先对可违约债券的违约前价值的表示问题进行讨论。我们将Xiong和Kohlmann（2012）[23]中的BSDE系统进行简化，得到了一个新的BSDE系统。我们给出了新BSDE系统的显式解(X,θ,X(0,T))并利用该显式解来刻画可违约债券的违约前价值，得到可违约债券的违约前价值的显式表达式。特别地，当违约强度为一个确定的连续函数时，，可违约债券的违约前价值有更加简化的形式。接着我们又讨论了CDS价格的动态演化问题。我们引入了一个比Xiong和Kohlmann（2012）[23]中更简化的BSDE系统。通过前面这两个BSDE系统的解，我们显式表示出CDS信用保障买方支付的保费。特别地，当违约强度和短期利率都为确定连续函数时，我们有结论：保费与时间无关，为一个确定常数。
[Abstract]:We assume that the instantaneous forward interest rate without default risk satisfies the HJM model without jump, introduce the positively bounded F- predictable default intensity process and introduce the relevant conclusions of domain flow expansion. Under the above assumptions, we first discuss the representation of the pre-default value of defaultable bonds. We simplify the BSDE systems in Xiong and Kohlmann (2012) [23] and obtain a new BSDE system. In this paper, we give the explicit solution of the new BSDE system (X, 胃 X (0T) and use the explicit solution to characterize the pre-default value of the defaultable bond, and obtain the explicit expression of the pre-default value of the defaultable bond. In particular, when the default intensity is a definite continuous function, the predefault value of the defaultable bond has a more simplified form. Then we discuss the dynamic evolution of CDS prices. We introduce a simpler BSDE system than Xiong and Kohlmann (2012) [23]. By the solutions of the above two BSDE systems, we express the CDS credit guarantee premium paid by the buyer. In particular, when both the default intensity and the short-term interest rate are deterministic continuous functions, we conclude that the premium is independent of time and is a definite constant.
【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;F224

【共引文献】