Statistical Inference For Hybrid CIR Model And Applications

Interest rate is a key factor in financial market.Researches on interest rate model are of far-reaching significance for interest rate to adjust the macroeconomic operation,maintain financial security and support economic development.Hence,this paper focus on the statistical inference for hybrid CIR model.Then the long-term characteristics of Shanghai Interbank Offered Rate are described by this model.First of all,the non-negativity for the solution of hybrid CIR model is presented.Then we prove that under some conditions,the hybrid CIR has the following properties:?)The solution of {Xt,rt}t?0 is ergodic if ?i=1n ?(?)?(?)>0;?)The solution of ?Xt,rt}t?0 is transient if ? i=1 n ?(i)?(i)<0;?)The solution of {Xt,rt}t?0 is null recurrent if ?i=1 n ?(?)?(?)=0.Finally,we use composite likelihood function and EM algorithm to estimate the parameters for the hybrid CIR model.In addition,we present the numerical simulation of the hybrid CIR model and an example of EM algorithm validation.Then,7-day Shanghai Interbank Offered Rate data is used for analysis.We use EM algorithm estimate parameters of the regression speed of interest rate,the long-term level of short-term interest rate,the diffusion coefficient and the probability of state transition.