Theoretical And Empirical Study On Value At Risk Forecast Combination

Financial risk management is the core task of financial institutions. As thebenchmark measure of financial market risk, Value-at-Risk (hereafter, VaR)'s ac-curate computation is a challenge of researching. Forecast combination creates anew forecast by pooling information from multiple forecasts, which makes it to havepotential ability to improve the forecast performance. Given that multiple VaR fore-cast methods are available and the application of forecast combination is relativelysimple, forecast combination of VaR provides an attractive solution to this problem.This paper focus on VaR forecast combination. The purpose of this study is to buildthe theoretical base of VaR forecast combination and to provide a simple, scientificapplication method for VaR forecast combination. Linear forecast combination isconsidered in this paper. The main content of this paper include the discussion ofdiversification e?ect, the characteristic and in-sample estimation performance of themethod of determining weights, the parameter selection and the application proce-dure of VaR forecast combination.When the paper investigates the principle of diversification e?ect, the diversifi-cation e?ect under square loss and the diversification e?ect for quantile combinationare separately studied. Through considering forecast bias, the paper extends theanalysis about diversification e?ect of forecast combination under square loss andfinds the new condition for which simple average weight is optimal weight. As VaR isunobservable, the paper investigates indirectly traditional forecast bias and volatil-ity through analyzing exceed ratio and tick loss. Based on Monte Carlo simulation technology, the paper finds the special features about diversification e?ect of VaRforecast combination, set up the relation between diversification e?ect of VaR fore-cast combination and diversification e?ect of forecast combination under square loss.Meanwhile, the paper also finds the limitation of exceed ratio used for measuringVaR forecasting performance, which lies in the fact that one VaR forecast with largetraditional forecast bias and volatility can have very good forecast performance. Fur-thermore, the paper finds that tick loss is simply not the sum for traditional forecastbias and volatility but possibly happen the phenomena that the positive traditionalforecast bias might decrease the in?uence of large volatility.This paper studies the in-sample estimation performance of forecast combinationusing simple average weight and quantile regression weight via Monte Carlo simula-tion technology. Quantile regression weight includes four weight forms, which are thegeneral weight form without constraints on weight, the weight form of suppressingthe intercept, the weight form of constraining the sum of weights except interceptto unity and the weight form of constraining the sum of weights to unity and sup-pressing the intercept, respectively. Moreover, this paper investigates the in?uenceof constraints on weight and the characteristics of these four weight forms, and drawsthe conclusion that their is a significant in?uence for the constraints on weight andthe constraints can make it better for forecast combination to re?ect the spirit offorecast combination, which is helpful for selecting the suitable weight form.Based on the double checking of Monte carlo simulation and real data analysis,this paper investigates the issue of parameter selection of VaR forecast combination. In term of simple average weight, this paper studies the major factors(say, singleVaR and its number)which might in?uence forecast performance. As for quantile re-gression weight, this paper focuses on the selection of weight form except the majorfactors discussed in simple average weight. The comparison results show that addingcertain constraints on weight might significantly improve forecast performance andthese four forms are all useful. Furthermore, the issues of sampling window and sam-ple size are discussed for quantile regression weight, and some suggestions about theirselection are proposed. Based on these analysis, this paper discusses the parametersensitivity of forecast combination. Given that the forecast combination using simpleaverage weight has larger parameter sensitivity than the forecast combination usingquantile regression weight, this paper concludes that simple average weight shouldbe firstly tried and quantile regression weight should only be used after the failure ofthe simple average weight.This paper provides the application method of forecast combination, which drawsthe PDCA cycle tool from quality control. During the Plan phrase of PDCA cycle,this paper put forward three standards of selecting individual forecast in order tosimplify the application of forecast combination. The e?ectiveness of these threestandards has been verified by real data analysis. Furthermore, based on the relativeforecast performance of single VaR, this paper put up with three di?erent applica-tion suggestions, which are strongly suggested, general suggested and opposite, fordi?erent background.In the last part of this paper, this paper extends the application field of VaR forecast combination to the parameter selection of VaR and credit risk VaR. Throughthe analysis of forecast combination role on decreasing model risk of VaR and thediscussion of the risk profile of Chinese stock market, this paper points out that it hasspecial value for the application of VaR forecast combination in Chinese stock market.Moreover, this paper discusses the issue whether VaR can predict Subprime Crisisand the potential application of forecast combination in the future risk managementtechniques.This study makes us to know more about the principle of diversification andquantile forecast combination, extends the research on the constrained quantile re-gression and can instruct directly the practice of VaR forecast combination. It isnot di?cult to incorporate the study results into the current risk management sys-tems. The study results with wide application would produce significant economicand social benefits.