Bayesian Quantile Autoregressive Model And Applied In Measuring Hong Kong’s Hang Seng Index

Bayesian quantile regressive method is popular. More and more people research it at home and abroad. Bayesian quantile regressive method applied to measure financial risk is an important research subject. And calculate the value of VaR is the mainstream method to measure the financial market’s risk. This paper based on bayesian quantile regressive method sets up the model of VaR, using the method to measure VaR of Hong Kong’s hang seng index.The first chapter elaborates the selected topic background and significance of research, and overviews the refrences at home and abroad.The second chapter is a brief overview of basic concepts and methods, including quantile regression, relevant theories and methods of the bayesian analysis, as well as the concept and main properties of VaR.The third chapter theoretically constructs framework of VaR model based on bayesian quantile regression. This chapter is divided into two parts. The first part, in view of the error subjects to asymmetric laplace distribution (ALD) and error subjects to asymmetric exponential power distribution (AEPD) on the model of quantile regression, by setting prior distribution of parameters and determining the likelihood function of samples, according to the principle of the bayesian, using MCMC algorithm, according to the full conditional distribution of the parameters, we get a sample implementation of markov chains with stationary distribution.The stationary distribution is the posterior distribution of parameters. Due to loss of mean square error, the optimal bayesian estimation of the parameters is the posterior mean, so the sample mean of markov chains can be used as the parameter of the optimal estimate. Worth mentioning is that because of ALD and AEPD are not standard distributions, before sampling, this paper deals with their likelihood functions. The second part, we construct the VaR model of bayesian quantile autoregression as a special type of the model of bayesian quantile regression. The particular way is:after the quantile regression VaR model being put forward, we set order of the model according to the AIC. We estimate parameters by the method of bayesian which is mentioned in the first part, and show the evaluation method of the VaR model under different quantile level.In the fourth chapter, the bayesian quantile autoregressive VaR model is applied to measure the risk of the hang seng index in Hong Kong based on the theoretical framework which is given in chapter 3. We take the yield rate of Hong Kong’s hang seng index from January 4,2010 to January 10,2014 as data. We analyze characteristics of the data from the mean, standard deviation, skewness, kurtosis, JB statistics, ADF value and autocorrelation coefficient and partial correlation coefficient. We find that the data has the characteristics of non-normal, rush thick tail, stationarity and the correlation. Then we can determine the model type belongs to bayesian quantile autoregressive VaR model which is mentioned in the third chapter. According to the third chapter, at first, we apply AIC to determine the order of model is five. Then, pick the chi-square distribution as prior distribution of σ, and the rest of parameters’prior distributions are normal distribution. In accordance with section 3.1 and section 3.1 the likelihood function and bayesian theory, we use MCMC algorithm and the R2WinBUGS in R language to get the consequences. We can get parameters’estimation of bayesian quantile regressive VaR model based on Hong Kong’s hang seng index at the levels of 0.01,0.025 and 0.05 respectively, the parameters of the posterior density map, dynamic iterative convergence and GR statistics graph. The results of analysis shows that the bayesian quantile autoregressive VaR model based on ALD and the bayesian quantile autoregressive VaR model based on AEPD at different quantile levels of markov chains are convergent, and the parameter’s estimations of error are small. Moreover, we compare different lagged variables. According to the model, we can calculate the VaR values of Hong Kong’s hang seng index under different confidence level. By comparing the real and estimated value of VaR, we can know that most real value of VaR is less than the estimated one which means that most of the losses are under the prediction. At the same time, the higher the confidence level, the estimation is more conservative and the smaller possibility of the real value beyond the predicted.The chapter five uses the Kupiec failure rate test method. We use this method to evaluate two VaR models which are built in the fourth chapter. We compare these two models through the failure interval, the number of failure, the failure rate, LR values and LR critical value. The results show that the VaR model which is based on AEPD has less failures and less failure rate than the VaR model which is based on ALD. And we compare the VaR model which is based on AEPD with historical simulation method. The results show that the VaR model which is based on AEPD is better.The sixth chapter summarizes the research conclusion of this paper, and looking for the future of the research.