The Theory And Application Of Term Structure Model With Jumps

In this dissertation, we mainly investigate the property of a term structure model of interest rate with jump diffusion, the existence and simulation of the numerical so-lution of the interest rate model with jump diffusion, and an empirical analysis on the date of Chinese interest market. This dissertation consists of five parts. As follows are main contents.In the foreword, the main actuality of domestic and foreign investigation about in-terest rate term structure models, and what this dissertation want to do are introduced.In chapter one, some mathematics knowledge about this area is introduced. It includes the introduction about the coefficient's functions and the theorems that will be used in the following dissertation.In chapter two, we mainly introduce some mathematics property about the inter-est rate model with jump diffusion. It includes the existence of global solution, the boundary of the solution and first moment, and the convergence of first and second moment.In chapter three, we mainly investigate the existence and simulation of numerical solution. In this dissertation, what we mainly investigate is the CKLS model with jump diffusion, so when we investigate the property of the model, we must take the condition that the coefficient's function doesn't satisfy linear growth condition. The conclusion is that, the numerical solution exists. Then we use Matlab to simulate the numerical solution.In chapter four, combined the interest rate market of China, an empirical analy-sis is given. Maximum Likelihood Estimation (MLE) method is used to estimate the CKLS model with jump diffusion, by using the data of bond redemption interest rate of China.