The Application Of Non-Parametric Statistics In Financial Risk Management

VaR is a method which is used to quantify the market risk. This method takes the theory of probability as the foundation and utilizes modern statistical analysis technology. Since it has been introduced, it is optimized and improved unceasingly, and obtains the considerable development. The central content of the VaR method is the estimate to the volatility. The massive empirical study indicates that many characteristics exist in the returns ratio sequence of the financial assets, such as"Leptokurtosis","Volatility clustering"and"leverage effect"and so on. So when we survey the financial risk with the time sequence model which is under the general parameter distribution supposition (E.g. a GARCH model), the deviation between its fitting fluctuation rate and the actual value is very huge. The most prominent merit of the non-parameter statistics lies in no hypothesis to the data's dispersion pattern, and the method of the nuclear density estimate can catch the statistical characters of the financial data fully. This article mainly makes the improvement to the traditional VaR model by using the modern method of non-parameter statistical.(1)The Non-parametric kernel density estimate and the partial linear estimate theory are summarized systematically. In view of the multi-collinearity exiting in the non-parameter regression, and in the contrast with the processing method in the parameter statistical inference, we propose the method of principal components partial linear estimate. Then it gives the simulation confirmation and the example analysis. (2)The risk measuring technique of VaR which is widely used is introduced in detail. Two commonly used tests of the VaR: Kupiec failure rate test and Quantile Loss test also are introduced. On the basis of the parameter GARCH method and the principle of the non-parameter partial linear estimate, the VaR Computation steps of non-parameter GARCH method are inferred to stock market returns. By the empirical analysis to card composite index and make the comparison with the related parameter methods, we draw the following conclusion: the returns sequence of the Shanghai composite index has the intense GARCH effect, and the VaR which is obtained by the non-parameter GARCH method, can be able to measure stock market's risk effectively under the given significance level.(3) Embarking from the basic method of Historical simulation, using volume as the weight to returns, and considering the factor of variance changing along with time, we propose one kind VaR model which takes the non-parametric kernel density estimate to the distribution of monetary assets returns as the foundation. Using copper stock contract data and by making the contrast with the other historical simulation method, it finally prove that the new method remains the merit of the historical simulation method, and can forecast the extreme case which will occur in the future effectively.Finally, we summarize this article's work, and propose the direction of the further research.