Solutions Of Jump-diffusion CKLS Model Under Regime Switching And Applications In Finance

This paper establishes a Jump-diffusion CKLS model under regime switching via incorporating regime switching and Poisson process into CKLS short-term interest rate model.We study solutions of Jump-diffusion CKLS model under regime switching and applications in finance.In theory,under the conditions of ?>1,by using Lyapunov function method,the existence and uniqueness of global positive solution of Jump-diffusion CKLS model under regime switching are proved and analytical properties of the solution including the boundedness of moment,stochastic boundedness and path estimation are given;by using Euler-Maruyama discretization method,numerical solutions of such a model are derived,and it is shown that numerical solutions converge to the 1 theoretical solution of the model.Under the conditions of ?=1/2,we prove that there is a unique non-negative solution of Jump-diffusion CKLS model under regime switching by constructing auxiliary function and using related properties of auxiliary functions;in addition,by using Euler-Maruyama discretization method,numerical solutions of such a model are derived,and convergence of Euler-Maruyama numerical solutions in L1 and L2 is considered.In applications,the convergence result of numerical solutions of Jump-diffusion CKLS model under regime switching is applied to a bond pricing problem and the expected return problem of a barrier option.Through numerical simulation,the reliability of Jump-diffusion CKLS model under regime switching is checked.Based on empirical analysis of 7-day Shibor interest rate,Jump-diffusion CKLS model under regime switching is more valid and effective for modeling dynamic interest rate in China 's financial market.