基于多分辨率分析和极值理论的集合VaR模型

doi:10.3969/j.issn.0253-2778.2016.11.008

中国科学技术大学学报 ›› 2016, Vol. 46 ›› Issue (11): 928-938.DOI: 10.3969/j.issn.0253-2778.2016.11.008

• 论著 • 上一篇

基于多分辨率分析和极值理论的集合VaR模型

王传好，方兆本，韩宇

中国科学技术大学管理学院统计与金融系，安徽合肥 230026

收稿日期:2015-11-03 修回日期:2016-05-19 接受日期:2016-05-19 出版日期:2016-05-19 发布日期:2016-05-19
通讯作者: 方兆本
作者简介:王传好，男，1988年生，硕士生. 研究方向：金融工程. E-mail: wchgood@mail.ustc.edu.cn
基金资助:
国家自然科学基金（71371007）资助.

Systematic VaR model based on multi-resolution analysis and extreme value theory

WANG Chuanhao, FANG Zhaoben, HAN Yu

Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

Received:2015-11-03 Revised:2016-05-19 Accepted:2016-05-19 Online:2016-05-19 Published:2016-05-19

摘要/Abstract

摘要： 为了捕捉金融资产价格波动的多尺度时变特征，利用多分辨率分析（multi-resolution analysis,MRA）将收益率序列分解成不同时域上的正交分量，并对各分量序列分别建立适当的ARMA-GARCH模型，在此基础上引入极值理论（extreme value theory,EVT）对收益率的厚尾性进行建模，构建了一种MRA-EVT模型.将该模型应用于沪深300指数的VaR预测.实证研究结果表明，与传统ARMA-GARCH模型、无条件EVT模型和MRA模型相比，该MRA-EVT模型显著提高了VaR的预测绩效.

关键词: 多分辨率分析, GARCH模型, 极值理论, VaR

Abstract: In order to capture time-varying features of volatility of asset price, multi-resolution analysis (MRA) was used to decompose financial returns into orthogonal components in different time domains. For each component, a certain ARMA-GARCH model was built. Extreme value theory (EVT) was then introduced so as to model the fat-tail of financial returns, and an MRA-EVT model was constructed. Finally, the proposed model was applied to predict VaR of CSI 300 index, and compared with traditional models, such as ARMA-GARCH model, unconditional EVT model and MRA model. Empirical results show that the MRA-EVT model significantly improves the accuracy of VaR estimation.

Key words: multi-resolution analysis, GARCH model, EVT, VaR

中图分类号:

F830.

王传好，方兆本，韩宇. 基于多分辨率分析和极值理论的集合VaR模型[J]. 中国科学技术大学学报, 2016, 46(11): 928-938.

WANG Chuanhao, FANG Zhaoben, HAN Yu. Systematic VaR model based on multi-resolution analysis and extreme value theory[J]. Journal of University of Science and Technology of China, 2016, 46(11): 928-938.

参考文献

[1] JORION P. Value at Risk: The New Benchmark in Controlling Market Risk[M]. Chicago：Irwin Professional Publishing, 1997.
[2] DUFFIE D, PAN J. An overview of value at risk[J]. The Journal of Derivatives, 1997, 4(3): 7-49.
[3] BOUCHAUD J P, POTTERS M. Theory of Financial Risk[M]. Paris: Alea-Saclay, Eyrolles, 1999.
[4] LI D. Value at Risk Based on the Volatility, Skewness and Kurtosis[EB/OL].[2015-10-03]. http://www.gloriamundi.org.
[5] CHAPPELL D, DOWD K. Confidence intervals for VaR[J]. Financial Engineering News, 1999, 9: 1-2.
[6] FAN J, GU J. Semiparametric estimation of value at risk[J]. The Econometrics Journal, 2003, 6(2): 261-290.
[7] 刘向丽,成思危,汪寿阳,等. 参数法,半参数法和非参数法计算我国铜期货市场VaR之比较[J]. 管理评论，2008,20(6): 3-8.
LIU Xiangli, CHENG Siwei, WANG Shouyang，et al. The comparison of Chinese copper futures market VaR estimation using parametric method, semiparametric method and nonparametric method[J]. Management Review, 2008,20(6): 3-8.
[8] DAVISON A C, SMITH R L. Models for exceedances over high thresholds[J]. Journal of the Royal Statistical Society, Series B (Methodological), 1990, 52(3): 393-442.
[9] DANIELSSON J, DE VRIES C G. Tail index and quantile estimation with very high frequency data[J]. Journal of Empirical Finance, 1997, 4(2): 241-257.
[10] NEFTCI S N. Value at risk calculations, extreme events, and tail estimation[J]. The Journal of Derivatives, 2000, 7(3): 23-37.
[11] JONDEAU E, ROCKINGER M. Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements[J]. Journal of Economic Dynamics and Control, 2003, 27(10): 1 699-1 737.
[12] GILLI M, KELLEZI E. An application of extreme value theory for measuring financial risk[J]. Computational Economics, 2006, 27(2): 207-228.
[13] CHRISTOFFERSEN P, GONCALVES S. Estimation risk in financial risk management[R]. CIRANO Working Papers, 2004.
[14] CHRISTOFFERSEN P. Evaluating interval forecasts[J]. International Economic Review, 1998, 39: 841-862.
[15] 林宇,黄登仕,魏宇. 胖尾分布及长记忆下的动态 EVT-VaR测度研究[J]. 管理科学学报,2011,14(7): 71-82.
LIN Yu, HUANG Dengshi, WEI Yu. Study on financial markets dynamic EVT-VaR measuring based on fated-tail distribution and long memory volatility[J]. Journal of Management Sciences in China, 2011, 14(7): 71-82.
[16] 杨超,李国良,门明. 国际碳交易市场的风险度量及对我国的启示——基于状态转移与极值理论的VaR比较研究[J]. 数量经济技术经济研究,2011,28(4): 94-109.
YANG Chao, LI Guoliang, MENG Ming. Risk measurement of the international carbon trading market and enlightenment to China[J]. The Journal of Quantitative & Technical Economics, 2011, 28(4): 94-109.
[17] CHAVEZ-DEMOULIN V, EMBRECHTS P, SARDY S. Extreme-quantile tracking for financial time series[J]. Journal of Econometrics, 2014, 181(1): 44-52.
[18] MCNEIL A J, FREY R. Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach[J]. Journal of Empirical Finance, 2000, 7(3): 271-300.
[19] ALLEN D E, SINGH A K, POWELL R J. EVT and tail-risk modelling: Evidence from market indices and volatility series[J]. The North American Journal of Economics and Finance, 2013, 26: 355-369.
[20] 李强,周孝华,张保帅. 平稳序列的 GPD 模型在风险测度中的应用[J]. 统计与决策,2013 (11): 78-82.
[21] BERGER T. Financial Crisis, VaR forecasts and the performance of time varying EVT-Copulas[C]// Operations Research Proceedings 2012. Springer International Publishing, 2014: 35-40.
[22] 张冕,万建平,李楚进. 小波理论在VaR计算中的应用[J]. 应用数学,2002,15（suppl）: 116-119.
ZHANG Mian, WAN Jianping, LI Chujin. A application of wavelets theory in VaR[J]. Mathematica Applicata, 2002,15（suppl）: 116-119.
[23] DU MOUCHEL W H. Estimating the stable index α in order to measure tail thickness: A critique[J]. The Annals of Statistics,1983,11(4):1 019-1 031.
[24] 彭选华. 金融风险价值量化分析的模型与实证[D]. 重庆：重庆大学,2011.
[25] 严纲. 基于小波方法的系统风险多尺度分析[D]. 兰州：兰州商学院,2013.
[26] HE K, WANG L, ZOU Y, et al. Value at risk estimation with entropy-based wavelet analysis in exchange markets[J]. Physica A: Statistical Mechanics and Its Applications, 2014, 408: 62-71.
[27] MALLAT S. A theory for multiresolution signal decomposition: The wavelet representation[J]. IEEE Pattern Anal and Machine Intell, 1989，11(7): 674-693.
[28] PERCIVAL D B, WALDEN A T. Wavelet methods for time series analysis[M]. Cambridge, UK: Cambridge University Press, 2006.
[29] FERNANDEZ V. Risk management under extreme events[J]. International Review of Financial Analysis, 2005, 14(2): 113-148.
[30] 许启发,蒋翠侠,张世英. 基于小波多分辨分析的协整建模理论与方法的扩展[J]. 统计研究,2007,24(8): 92-96.
XU Qifa, JIANG Cuixia, ZHANG Shiying. Expansion of modeling theory and method for cointegration based on wavelet multiresolution analysis[J]. Statistical Research, 2007, 24(8): 92-96.

基于多分辨率分析和极值理论的集合VaR模型

Systematic VaR model based on multi-resolution analysis and extreme value theory

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