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CN 34-1054/N

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

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

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2016.11.008
  • Received Date: 03 November 2015
  • Accepted Date: 19 May 2016
  • Rev Recd Date: 19 May 2016
  • Publish Date: 30 November 2016
    Abstract

  • 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.

    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.
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    • References(30)
  • [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.
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    [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.
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