Pricing The Defaultable Bond Of Corporation Under The Structural Model With Jump Risks

The credit Risk has been a very important research topic in mathematical Finance. One of the key work of the credit risk management is the pricing problem on the defaultable bonds. The corporate bonds as a defaulted risk securities, it is an issued debt obligation that shows the enterprise to raise external capitals. When the corporate total values asset are not sufficient to pay its debts, defaultable will happen. In the modern financial theory study on the company bonds is mainly divided into two the approaches which include the structural approach and the reduced-form approach. In the actual financial market, However, a more practical and effective market model plays a significant role in investment decision, risk aversion and management. The classical Black-Scholes Model has more advantages and practical meanings, but too idealistic in the assumptions, these lead to a large deviation between the theoretic results and observed date. In order to be able to depict the variables of the actual reasonable market changing rules, modifying the classical Black-Scholes model to be consistent with the actual market changing is provided by many scholars, try to establish better fitting the financial market of the mathematics model. In1974, Merton firstly established corporate total values asset structure model and make a research on company bonds. Based on the Merton’s work, many scholars had further research and gained abundant achievements. These research mainly focuses on the behavior in modeling of corporate assets, they are jump diffusion process, stochastic volatility and stochastic interest rate and so on, which close to actual mathematical model. In this article,based on the structural approach, this paper consider the underlying assets following the jump-diffusion model which both the volatility and interest rate contain jumps, and the discuss the price of defaultable bonds. This model has general and realistically. The main contributions are as follows:Chapter1Firstly provides an introduction to the necessity of the research on the pricing of the defaulted bonds.Futhermore, the motivations and main study topics of this dissertation are introduced.Chapter2Discuss the pricing of company defaulted bonds under the interest rate with jump. By applying Fourier inversion transform, practical differential equation and Feynman-Kac theo-rem,we get the closed form about the defaulted bond prices. Finally some numerical examples are provided by parameters on the effect of defaulted bond prices.Chapter3Consider the pricing of the defaulted bonds under the stochastic volatility with jump on the Chapter2.By applying practical differential equation, Riccati function and Feynman-Kac theorem, we get the closed form about the defaulted bond prices. We analyze the sensitiveness of volatility by some numerical examples.In Chapter4We sum our main conclusions and suggestions for further research.