The Application Of Hierarchical Dirichlet Process In The Market Risk Measurement Of Stock Market

The management of the market risk of the stock market has great significance,which is related to individual investors’ capital safety,institutional investors’ return on investment,the regulators’ supervision system and the steady development of the whole financial market and the society,however,the effective management of the market risk of the stock market is dependent on the accurate measuring of market risk.The current measurement models of market risk of stock market mainly include Value-at-Risk(VaR)model and Conditional Value-at-Risk(CVaR)model.The concept of VaR is simple.It can measure the risk of asset with a single number but it isn’t a consistency measurement tool.What’s more,it can’t cover all the tail risk well.However,CVaR realizes the cover of tail risk by considering the conditional mean of losses exceed Va R.VaR and CVaR are widely used in the measurement of the market risk of the stock market.The calculation methods of these two models involve parametric method,nonparametric method and semiparametric method,Bayesian nonparametric method is the leading edge method.The popular prior distribution of Bayesian nonparametric method includes Dirichlet Process(DP),Hierarchical Dirichlet Process(HDP)and so on.The Dirichlet process has been applied to the measurement of market risk of stock market and showed excellent performance.This paper goes further,set the Hierarchical Dirichlet process as the prior distribution of stock return distribution,so as to share data among similar stocks,then the return distribution are fitted adaptively accoding to these data.This paper firstly apply Hierarchical Dirichlet Process model to simulation data of the complex distribution and fat-tailed distribution,the estimated results of parameters are hightly similar to that of real distribution,verifying the effectiveness of this method in estimating complex distribution and fat-tailed distribution.Then,this method is applied to measuring the market risk of three stocks from the Shenzhen Stock Exchange and three stocks from the NewYork Stock Exchange,gettting the fitted stock return distribution by Hierarchical Dirichlet Process model,we use the Monte Carlo simulation method to calculate the VaR and CVaR,and the results are compared with that of t distribution,Generalized Error distribution(GED),Generalized Pareto Distribution(GPD)and Generalized Auto Regressive Conditional Heteroskedasticity(GARCH)model.Finally,based on the results of empirical researchs,this paper draws the following conclusions: Althought there are many differences between the stock market of China and the US,Hierarchical Dirichlet Process model always can capture the fat tail of the stock return distribution,the estimated results of the market risk based on Hierarchical Dirichlet Process model is more robust than that of t distribution,GED distribution,GPD distribution and GARCH model.And between VaR and CVa R,the estimated results of CVa R are more robust than the VaR,whose risk coverage is more comprehensive.To this end,this paper proposes the following suggestions for the management of market risk of stock market: The Hierarchical Dirichlet Process model can be applied to the measurement of market risk of stock market,which is conducive to improving the accuracy and robustness of the estimated results and thus better managing the market risk of stock market.As for the selection of Va R and CVaR,it can be decided according to the management goal.Compared with VaR,CVaR is more conservative,which is more suitable for the risk managers that have conservative goal.