The Theory and Application of Term Structure Model with Jumps
|Course||Probability Theory and Mathematical Statistics|
|Keywords||With jumps and interest rate term structure model Jump-diffusion stochastic differential equations Euler-Maruyama method Maximum likelihood estimation Bond repurchase rate|
This paper studies the nature of the interest rate term structure model with jumps , the existence of the numerical solution and numerical solution simulation, and empirical analysis combined with China 's bond market . Text is divided into five parts , the main contents are as follows: the preamble , introduces the current research status at home and abroad of the interest rate term structure model , and in this article to be carried out on the basis of research first chapter introduces this article to study the mathematical theory of knowledge , including the interest rate term structure model coefficient functions and parameters Institute needs an introduction , the nature of the interest rate term structure model theorem second chapter focuses on the the various mathematical nature of the interest rate term structure model , specifically the existence of global solution , the solution and the first moment bounded , as well as in a variety of conditions the next order moment and the second moment convergence . third chapter , the existence of the numerical solution of the main research , as well as the numerical solution of the interest rate term structure model simulation . research CKLS model coupled with a jump factor ( ? ) the CKLS model , the coefficients of the model function does not satisfy the linear growth condition , so study the existence of the numerical solution when we should be taken into account that , the final conclusion is that the values ??of the model solution exists . then given a numerical solution of the term structure model simulation with Matlab . fourth chapter , mainly with the status quo of China 's interest rate , with the CKLS model with jumps bond repurchase rate of the seven day period an empirical analysis parameter estimation method is used in the empirical analysis of maximum likelihood estimation .