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Predicting extreme VaR: Nonparametric quantile regression with refinements from extreme value theory

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  • Schaumburg, Julia

Abstract

This paper studies the performance of nonparametric quantile regression as a tool to predict Value at Risk (VaR). The approach is flexible as it requires no assumptions on the form of return distributions. A monotonized double kernel local linear estimator is applied to estimate moderate (1%) conditional quantiles of index return distributions. For extreme (0.1%) quantiles, where particularly few data points are available, we propose to combine nonparametric quantile regression with extreme value theory. The out-of-sample forecasting performance of our methods turns out to be clearly superior to different specifications of the Conditionally Autoregressive VaR (CAViaR) models.

Suggested Citation

  • Schaumburg, Julia, 2010. "Predicting extreme VaR: Nonparametric quantile regression with refinements from extreme value theory," SFB 649 Discussion Papers 2010-009, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2010-009
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    References listed on IDEAS

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    1. James W. Taylor, 2008. "Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 382-406, Summer.
    2. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    3. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89.
    4. Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
    5. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    6. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    7. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(5), pages 793-813, December.
    8. Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Oxford University Press, vol. 3(2), pages 227-255.
    9. Yu, Keming & Jones, M. C., 1997. "A comparison of local constant and local linear regression quantile estimators," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 159-166, July.
    10. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 75, European Central Bank.
    13. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
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    Cited by:

    1. Her-Jiun Sheu & Chien-Ling Cheng, 2011. "Systemic risk in Taiwan stock market," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 13(5), pages 895-914, August.
    2. Chao, Shih-Kang & Härdle, Wolfgang Karl & Wang, Weining, 2012. "Quantile regression in risk calibration," SFB 649 Discussion Papers 2012-006, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    4. Ioan Trenca & Simona Mutu & Nicolae Petria, 2011. "Econometric Models Used For Managing The Market Risk In The Romanian Banking System," Analele Stiintifice ale Universitatii "Alexandru Ioan Cuza" din Iasi - Stiinte Economice (1954-2015), Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, vol. 2011, pages 115-123, july.
    5. repec:hum:wpaper:sfb649dp2012-006 is not listed on IDEAS
    6. Lesedi Mabitsela & Eben Maré & Rodwell Kufakunesu, 2015. "Quantification of VaR: A Note on VaR Valuation in the South African Equity Market," JRFM, MDPI, vol. 8(1), pages 1-24, February.

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    More about this item

    Keywords

    Value at Risk; nonparametric quantile regression; risk management; extreme value theory; monotonization; CAViaR;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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