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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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    Cited by:

    1. repec:hum:wpaper:sfb649dp2012-006 is not listed on IDEAS
    2. 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.
    3. 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.
    4. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    5. 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.
    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.

    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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