Analysis And Research With The Simulation And Parameter Estimation Of CIR Model

In financial markets, interest rate is the determinant of asset pricing and risk management. Therefore, carrying on study of interest rate model has important significance.This paper mainly studies the simulation and parameter estimation with the interest rate model of CIR. The analysis of the parameter estimation is based on the exact simulated data for its good simulation performance. There are no significant difference found among the general estimates methods for the estimated effect. The time interval ?t only has influence on the estimated effect of volatility σ but affects the estimated effect of parameters μ and α weakly. The interval length T is the main factor that influences the estimated effect. Particularly, the estimation of α is strongly dependent on T and the effect is very poor when T is small, which is due to the fact that α respects the recovery rate.In view of the above analysis, this paper takes the Bayesian estimation based on Markov Chain Monte Carlo(MCMC) methods to estimate the parameters and slightly improves the estimated effect of α. Then we proposed the indirect Bayesian estimation method that including Maximum a posteriori estimation(MAP) and the posterior mean estimation based on the exact likelihood function. It improves the estimated effect of α remarkably when T is small.