Jump - Diffusion Under The Conditions Of Corporate Bond Default Pricing Model

Along with the progress of global science and technology and the development of politics and economy, cerdit risk is growing expponentia-lly. So we take more and more attention to credit risk which plays an important part in risk management and pricing financial products. And the pricing of default bonds is the core of credit risk management.In this paper, it introduces the background and construction methods of structual model and insurance actuary pricing model.Then it solves the problem of pricing corporate bond with default through expanding the model we mentioned before by changing the assumed condition. In view of traditional structural model, this paper assumes the firm value process is a jump-diffusion model and builds the pricing model of corporate bond with default using the theory of no-arbitrage pricing.This model is discussed under two assumptions, the default threshold is constant and then it is a function of time. By solving the differential equations of equity value under the two cases, the article obtains the pricing formulas respectively. Then it discusses the default probability,credit spreads and the impacts of each parameter on them. When the default threshold is a random process with jump, this paper discribes it as the firm debt and assumes that both the firm value and the firm debt are non-homogeneous poisson jump-diffusion processes.Then pricing model of the corporate bond which may default only at maturity is built respectively by using actuarial approach when the two processes mentioned before are indepen-dent or not,and the pricing formula is obtained at last by sovling the model.