Numerical Simulation Of Statistical Behavior For Fractional Cox-Ingersoll-Ross Process

Cox-Ingersoll-Ross(CIR)process has important applications in the field of finance.In this paper,the statistical behavior of the fractional CIR process is simulated and discussed.Since there is no analytical solution for the CIR process,in order to explore its numerical solution,the fractional Brownian motion is simulated by using WFBM function,and the expectation and variance of the process are simulated by using EM method.In order to further study the fractional CIR process,another function FBM1D was used to simulate the fractional Brownian motion,and Lamperti transformation of the fractional CIR process was used to obtain the auxiliary equation.The numerical solution of the fractional CIR process by backward Euler method was simulated,and the simulation results were compared with the explicit scheme.It is found that both have a strong degree of fitting.In order to analyze the differences between the two functions,we observe and compare the variance loglog graphs of the fractional Brownian motion increments of functions.Finally,by controlling the time variables,it is found that the mean value of the fractional CIR process is still bounded with respect to time in the fractional CIR model when the adjusting speed parameter is greater than 0,and the distribution of the fractional CIR process converges to a unique limit distribution when the time tends to infinity.In order to further verify the superiority of the proposed algorithm and compare the two functions,the OU processes with analytical solutions are simulated.Through comparison of images and data,the numerical solutions,expectations and variances of the fractional OU processes simulated by EM method and the theoretical analytical solutions,expectat,ions and variances also have a strong degree of fitting.The FBM1D and WFBM show little difference in the expectation of the simulated fractional OU process,but the FBM1D is more fit than WFBM in the simulated variance.To a certain extent,it is appropriate to simulate fractional Brownian motion with function fbmld and to simulate numerical solution,expectation and variance of fractional CIR process with EM method.