The stylized facts of financial markets, such as volatility clustering, fat tail and asymmetry, make the multiperiod VaR do not comply with simple "rule of time root" in one period VaR measure. Therefore, a more reasonable method is need to seek to evaluate multiperiod VaR accurately. Multiperiod VaR is mainly influenced by two variables, i.e. holding period and volatility. To determine the impact model (linear or nonlinear) of the two variables is essential for evaluating VaR accurately. Nonlinear quantile regression model, overcoming the limitations of the linear quantile regression model in describing linear dependence between multiperiod VaR and its influencing factors, can be used to improve the accuracy of VaR. Three types of methods, volatility model, QRNN+volatility model, and SVQR+volatility model, for evaluating multiperiod VaR has been proposed in this paper based on volatility modeling and nonlinear quantile regression method. For empirical application, three stock price indices are selected: Shenzhen Composite Index, Hang Seng Index and S&P 500 from 19 Jan. 2011 to 28 Sep. 2012. Six different volatility models are considered and two types of nonlinear quantile regression models are combined with them. As a result, the 18 kinds of methods in multiperiod VaR measure are compared together. The empirical results show that volatility model has an influence on the effect of multiperiod VaR measure. In terms of the accuracy of VaR measure, the SVQR+volatility model is slightly better than QRNN+volatility model, and both of them are superior to the volatility model. The good performance of the nonlinear quantile regression models in VaR evaluation comes from the fact that the QRNN and SVQR models belong to nonparametric methods. They have the ability to discover a complex nonlinear relationship among variables without specifying a explicit functional form. This property is very useful for exploring the unknown relation among financial variables.
XU Qi-fa, ZHANG Jin-xiu, JIANG Cui-xia
. Evaluating Multiperiod VaR via Nonlinear Quantile Regression Model[J]. Chinese Journal of Management Science, 2015
, 23(3)
: 56
-65
.
DOI: 10.16381/j.cnki.issn1003-207x.2015.03.007
[1] Jorion P. Value at risk: The new benchmark for managing financial risk[M]. New York: McGraw-Hill. 2007.
[2] Morgan J, Riskmetrics: Technical document. Working Paper, Morgan Guaranty Trust Company of New York, 1996.
[3] Koenker R, Bassett G W. Regression quantiles[J]. Econometrica, 1978, 46(1): 33-50.
[4] Taylor J W. Using exponentially weighted quantile regression to estimate value at risk and expected shortfall[J]. Journal of Financial Econometrics, 2008, 6(3): 382-406.
[5] 张瑞锋, 张世英, 唐勇. 金融市场波动溢出分析及实证研究[J]. 中国管理科学, 2006, 14(5): 14-22.
[6] 史金凤, 刘维奇, 杨威. 基于分位数回归的金融市场稳定性检验[J]. 中国管理科学, 2011, 19(2): 24-29.
[7] 许启发, 蒋翠侠. 分位数局部调整模型及应用[J]. 数量经济技术经济研究, 2011, 28(8): 115-133.
[8] 陈磊, 曾勇, 杜化宇. 石油期货收益率的分位数建模及其影响因素分析[J]. 中国管理科学, 2012, 20(3): 35-40.
[9] Taylor J W. A quantile regression approach to estimating the distribution of multiperiod returns[J]. Journal of Derivatives, 1999, 7(1): 64-78.
[10] Taylor J W. A quantile regression neural network approach to estimating the conditional density of multiperiod returns[J]. Journal of Forecasting, 2000, 19(4): 299-311.
[11] White H. Nonparametric estimation of conditional quantiles using neural networks[M]. New York: Computing Science and Statistics, 1992.
[12] Feng Yijia, Li Runze, Sudjianto A, et al. Robust neural network with applications to credit portfolio data analysis[J]. Statistics and its interface, 2010, 3(4): 437-444.
[13] Cannon A J. Quantile regression neural networks: Implementation in R and application to precipitation downscaling[J]. Computers & Geosciences, 2011, 37(9): 1277-1284.
[14] Cannon A J. Neural networks for probabilistic environmental prediction: Conditional density estimation network creation and evaluation (CaDENCE) in R[J]. Computers & Geosciences, 2012, 41(4): 126-135.
[15] Takeuchi I, Furuhashi T. Non-crossing quantile regressions by SVM. Proceedings of 2004 IEEE International Joint Conference on Neural Networks, Budapest,Hungary,July 25-29,2004.
[16] Li Youjuan, Liu Yufeng, Zhu Ji. Quantile regression in reproducing kernel Hilbert spaces[J]. Journal of the American Statistical Association, 2007, 102(477): 255-268.
[17] Shim J, Kim Y, Lee J, et al. Estimating value at risk with semiparametric support vector quantile regression[J]. Computational Statistics, 2012, 27(4): 685-700.
[18] Bollerslev T. Generalized autoregressive conditional heteroskedasticity[J]. Journal of Econometrics, 1986, 31(3): 307-327.
[19] Vapnik V N. The nature of statistical learning theory[M]. New York: Springer, 1995.
[20] Huber P J. Robust estimation of a location parameter[J]. Annals of Mathematical Statistics, 1964, 35(1): 73-101.
[21] Yuan Ming. GACV for quantile smoothing splines[J]. Computational Statistics and Data Analysis, 2006, 50(3): 813-829.
[22] Chen Meiyuan, Chen J E. Application of quantile regression to estimation of value at risk. Working Paper, National Chung-Cheng University, 2002.
[23] 王鹏, 魏宇. 中国燃油期货市场的 VaR 与 ES 风险度量[J]. 中国管理科学, 2012, 20(6): 1-8.
[24] Kupiec P. Techniques for verifying the accuracy of risk measurement models[J]. Journal of Derivatives, 1995, 3(2): 73-84.
[25] Christoffersen P F. Evaluating interval forecasts[J]. International Economic Review, 1998, 39(4): 841-862.
