基于马尔科夫随机波动和极值理论的风险测度

中国管理科学 ›› 2014, Vol. 22 ›› Issue (10): 44-51.

基于马尔科夫随机波动和极值理论的风险测度

姬新龙, 周孝华

重庆大学经济与工商管理学院, 重庆 400030

收稿日期:2012-12-28 修回日期:2013-05-12 出版日期:2014-10-20 发布日期:2014-10-20
作者简介:姬新龙（1982-），男（汉族），河南南阳人，重庆大学经济与工商管理学院博士，讲师，研究方向：金融风险管理.
基金资助:
国家自然科学基金资助项目（70473107）

Risk Measurement Based on Markov Stochastic Volatility and EVT

JI Xin-long, ZHOU Xiao-hua

School of Economics and Business Administration, Chongqing University, Chongqing 400030, China

Received:2012-12-28 Revised:2013-05-12 Online:2014-10-20 Published:2014-10-20

摘要/Abstract

摘要： 针对金融资产波动的时变、聚集以及状态转换等特征，将马尔可夫转换模型和随机波动模型相结合，同时考虑波动尾部的状态分布，构建MSSV-t模型，然后将收益序列转化为标准残差序列，在此基础上，应用EVT模型对标准残差进行建模，进而构建基于MSSV-t-EVT的VaR测度模型，最后对该模型的有效性进行检验。研究发现：MSSV-t-EVT模型能够有效识别上证指数（SSCI）的波动转换特征，并且能合理地测度该指数的收益风险，尤其在高的置信水平下表现更好。研究结论表明MSSV-t-EVT模型能较为准确的刻画股市剧烈波动的事实，可用于交易风险控制和对市场异常波动的预警。

关键词: MSSV-t模型, 极值理论, 波动状态转换, 风险测度

Abstract: In order to capture the characteristics of changed, gathered and state transitions of the fluctuations in financial assets in the stock returns data, Markov chain is introduced into the SV model to build the MSSV-t model, then the extreme value theory(EVT) is combined to measure the VaR. Use the Shanghai Composite Index for the empirical analysis. Finally the effect of MSSV-t-EVT model is analyzed with Backtesting, the results shows that the MSSV-t-EVT model can portray the fluctuation characteristics of financial yield effectively, especially the extreme fluctuation characteristics. Backtesting results shows, the application of MSSV-t-EVT model to measure the risk of comprehensive Index is reasonable and effective. In particular the higher the confidence level, the higher the accuracy.These results indicate that MSSV-t-EVT model has a better description and warning functions than the traditional linear risk measurement model. It can be used for the risk control of investment portfolio, and also for the warning of abnormal fluctuations by financial regulators.

Key words: MSSV-t model, extreme value, fluctuation state transition, risk measurement

中图分类号:

F831.5

姬新龙, 周孝华. 基于马尔科夫随机波动和极值理论的风险测度[J]. 中国管理科学, 2014, 22(10): 44-51.

JI Xin-long, ZHOU Xiao-hua. Risk Measurement Based on Markov Stochastic Volatility and EVT[J]. Chinese Journal of Management Science, 2014, 22(10): 44-51.

参考文献

[1] Bollerslev T. Financial econometrics:Past developments and future challenges[J]. Journal of Econometrics,2001,100(1): 41-51.

[2] Taylor S J. Stock price distributions with stochastic volatility: An analytic approach[J]. Review of Financial Studies,1982,4:727-752.

[3] Tauchen G E, Pitts M.The price variability-volume relationship on speculative Markets[J]. Econometrica,1983,51(2):485-505.

[4] 周孝华,张燕.一种新的风险价值(VaR)计算方法及其应用研究[J]. 管理学报, 2008,5(6):819-823

[5] 魏宇.股票市场的极值风险测度及后验分析研究[J]. 管理科学学报,2008,11(1):78-88.

[6] 詹原瑞,田宏伟.极值理论(EVT)在汇率受险价值(VaR)计算中的应用[J]. 系统工程学报,2000,15(1):44-52.

[7] 徐山鹰,杨晓光.风险价值的完全参数方法及其在金融市场风险管理中的应用[J]. 系统工程理论与实践,2001,21(4):74-79.

[8] 魏宇.金融市场的收益分布与EVT风险测度[J]. 数量经济技术经济研究,2006,23(4):101-110.

[9] Diebold F X.Modeling the persistence of conditional variances:A comment[J]. Econometric Reviews,1986,5(1):51-56.

[10] Lamoureux C G, Lastrapes W D.Persistence in variance,structural change,and the GARCH model[J]. Journal of Busines&Economic Statistics,1990,8(2):225-234.

[11] 蒋祥林,王春峰,吴晓霖.基于状态转移ARCH模型的中国股市波动性研究[J]. 系统工程学报,2004,19(3):270-277.

[12] 丁志国,苏治,杜晓宇.经济周期与证券市场波动关联性——基于向量SWARCH模型的新证据[J]. 数量经济技术经济研究,2007,24(3):61-68.

[13] Hwang S, Satchell S E, Pereira P L V. How persistent is volatility?An answer with markov regime switching stochastic volatility models[J]. Journal of Business Finance&Accounting,2007,34: 1002-1024.

[14] Shephard N. Statistical aspect of ARCH and stochastic volatility [M]. London: Chapman & Hall, 1996.

[15] Jacquier E, Polson N G, Rossi P E. Bayesian analysis of stochastic volatility Models[J]. Journal of Business and Economic Statistics, 2002,20(1):69-87.

[16] Chib S, Nardari F, Shephard N. Markov chains Monte Carlo methods for stochastic volatility models[J]. Journal of Econometrics, 2002,108(2): 281-316.

[17] Pickands J. Statistical inference using extreme order statistics[J]. The Annals of Statistics,1975,3(1):119-131.

[18] Lee T H, Saltoglub B. Assessing the risk forecasts for Japanese stock market[J]. Japan and the World Economy, 2002,14(1): 63-85.

[19] Garcia R, Perron P.An analysis of the real interest rate under regime shifts [J]. The Review of Economics and Statistics, 1996,78(1):111- 125.

[20] Mills T C, Wang Ping. Regime shifts in European real interest rates [J]. Review of world Economics,2003,139(1):66-81.

[21] Danielsson J, Devries C G.Value at risk and extreme returns[D]. London: London School of Economics,1997.

[22] Dupuis L A. The effect of various silvicultural treatments on amphibian assemblages of the Robert's Creek watershed. Ministry of Forests[R]. Vancouver Region, Interim report,1998.