Applicaton Of Mean Variance Change-point Model To Value-at-Risk

Value-at-Risk as the core of risk management has been widely used in many ways such as measuring risk and estimating risk. When it was introduced in measuring the stocks risk, we usually follow the assumption that the stocks return has a Normal distribution. On the assumption the key problem to compute Value-at-Risk is how to estimate the mean and variance of a certain stock. At present, on the Normal distribution, there are two main methods to estimate Value-at-Risk .One is ARCH /GARCH method, but the sort of those method has an obvious shortcoming is that these models based on the merely recent return data which have neglect the experience data. The other method is variety kinds of weighted mean and variance models. The basic principle of this kind of method is to divide all those data into several groups, then reckon mean and variance of each group and make the general estimated mean and variance is formed by the mean of mean and variance of each group. The main shortcoming of these method is which only weighed by simple sample mean and sample variance, which method is not involving any advanced statistics techniques, so the method can not give an estimation with high precision. In order to get over those disadvantages, at the same time, we take into account the reality of that the stocks return is changing over time, so when estimating stocks return we should use both the recent data and the experienced data, which is also determined by the character of stocks management has continuity and variability. So a new model named change-point model of mean and variance was introduce in this papers. We use the very model to calculate the Value-at-Risk of Shenzhen A stock, then we give corresponding knowledge of model test. The method of change-point model of mean and variance can give the real time estimation of mean and variance on the base of the recent data and the experienced data. Since the stocks return is known, we calculate Value-at-Risk of the stocks based on change-point model of mean and variance. At the same time, in order to show the rationality of our model, we introduce three ways of testing for this model: they are L -Test, B -Test, R -test and they all belong to the class of direct test method; moreover ,we also introduce two ways of indirectly testing: F ?Test and Possion Test. Finally we point out some improvability and considerable issue of our model.