The Parameter Estimation Of CEV Model Based On Markov Chain Mento Carlo Method

Because the Constant Elasticity of Variance(referred to as CEV) model could well describe "the volatility smile" phenomenon, it modified the Black-Scholes model's assumption about the constant volatility in some ways, therefore, we choose the CEV model to study. However, since the precise likelihood function expression of the CEV model is not easy to get, it is extremely difficult to estimate the parameter. Markov Chain-- Monte Carlo(MCMC) method which is based on Bayesian statistics, is a new solution to estimate the model's parameters. Compared with other parameter estimation methods,the MCMC method is easy to operate and it has higher parameter estimation accuracy.Based on the MCMC method of some scholars' study in stochastic volatility models,we try to use the MCMC method to estimate the parameters in CEV model, and then we choose the Shanghai and Shenzhen 300 stock index as the research object make an empirical analysis. First of all, using the GARCH(1, 1) model to fit the Shanghai and Shenzhen 300 stock index log-return data, we obtained the volatility in the Shanghai and Shenzhen 300 stock index log-return, then associate with the definition of constant elasticity of variance, calculate the prior distribution of the CEV model parameters'.Secondly,the MCMC method could be used in the CEV parameters estimation by WinBUGS software. From the result of the software, we know that the estimation results are consistent with the prior distribution, and the CEV model which is based on MCMC method is convergent, and then our parameter estimation is effective. Finally, compared with the the maximum likelihood estimation(MLE) and the generalized moment estimation(GMM), the results of the parameters estimation prove that the MCMC method MCMC method has higher estimation precision, and easier to implement.