The Research Of Exponential Jump Diffusion Credit Risk Model

Since the1980s, with the intensifying undulation of financial markets, the main cause of thebanks and enterprises bankruptcy is credit risk. Therefore, modeling credit risk has become a hot issueof the academic research. At the same time, the rapid development of probability theory, financialengineering and information science has provided technical support for modeling credit risk so thattwo main modern credit risk model have been formed: structural model and reduced model.In this paper, two aspects of exponential jump diffusion credit risk model has been extended tostudy under the structural framework and some conclusions have been obtained. First, the exponentialjump-diffusion credit risk model with time-dependent volatility is considered. By the martingaleapproach, an upper bound estimation of the default probability of the model is obtained when thematurity of the corporate bonds tends to infinity. Then, we deal with the exponential jump-diffusioncredit risk model with threshold dividend strategy. By the stochastic calculus, the integro-differentialequations with certain boundary conditions for the moment-generation function and the n-th momentof the discounted dividend payments prior to ruin are derived. Furthermore, we also derive theintegro-differential equations with boundary conditions for the expected discounted penalty functionsand the Laplace transform of the default time. Finally, as a example, the closed form expressions forthe Laplace transform of the default time when the jumps have double mixed exponential distributionare derived. Using the closed form expressions we obtain numerical solutions for the defaultprobability by Laplace numerical inversion.