Research Of Measure Of Value At Risk Of Financial Market Based On Bayesian Theory

VaR refers to the possibly biggest loss of financial assets under the fixed significance level of statistics during a certain period.The calculation method of VaR can be divided into parameters,half parameters,nonparameters.This paper mainly studies the parameter estimation method based on the GARCH mode.Assuming the return rate of financial asssets have specific distribution function,under the analysis framework of parameter estimation,VaR of financial assets during unit time equals to product of the quantile of the specific distribution function under a given significant level,the initial value of assets and the varance of return on assets.The accuracy of the estimation of the variance is directly related to whether VaR of the assets could be accurately calculated.Because the GARCH model can capture the fluctuation characteristics of return on financial assets well,in this paper,we use the GARCH model to simulate,estimation and prediction of the variance of return on assets.In terms estimation of GARCH model,there are two totally differenrt methods,one is the traditional maximum likelihood(ML),the other is markov chain monte carlo(MCMC)simulation algorithm based on bayesian theory.We collected the data of Shanghai stock index and shenzhen component index from 2008.1.2to 2015.12.31 to conduct empirical analysis.Using GARCH model to modeling of index variance,respectively,using the method of maximum likelihood and bayesian method estimated and predicted the GARCH model,then we used indictor of mean square error(MSE)and mean absolute error(MAE)to compare the accuracy of the two predicted sequence of variance.Emperical analysis supported that the error of predicted variance of Bayesian method is less than maximum likelihood method.Posterior test of VaR model by failure inspection suggests that the failure rate of Bayesian method was lower than maximum likelihood method.Practice showed that Bayesian has great advantage than maximum likelihood method.