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Quantile Regression and Value at Risk

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Handbook of Financial Econometrics and Statistics

Abstract

This paper studies quantile regression (QR) estimation of Value at Risk (VaR). VaRs estimated by the QR method display some nice properties. In this paper, different QR models in estimating VaRs are introduced. In particular, VaR estimations based on quantile regression of the QAR models, copula models, ARCH models, GARCH models, and the CaViaR models are systematically introduced. Comparing the proposed QR method with traditional methods based on distributional assumptions, the QR method has the important property in that it is robust to non-Gaussian distributions. Quantile estimation is only influenced by the local behavior of the conditional distribution of the response near the specified quantile. As a result, the estimates are not sensitive to outlier observations. Such a property is especially attractive in financial applications since many financial data like, say, portfolio returns (or log returns) are usually not normally distributed. To highlight the importance of the QR method in estimating VaR, we apply the QR techniques to estimate VaRs in International Equity Markets. Numerical evidence indicates that QR is a robust estimation method for VaR.

We thank Prof. C.-F. Lee for helpful comments. This project is partially supported by Boston College Research fund.

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Author information

Authors and Affiliations

  1. Department of Economics, Boston College, Chestnut Hill, MA, 02467, USA

    Zhijie Xiao

  2. Bertolon School of Business, Salem State University, Salem, MA, USA

    Hongtao Guo & Miranda S. Lam

Authors
  1. Zhijie Xiao
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  2. Hongtao Guo
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  3. Miranda S. Lam
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Corresponding author

Correspondence to Zhijie Xiao .

Editor information

Editors and Affiliations

  1. Department of Finance and Economics, Rutgers Business School, Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA

    Cheng-Few Lee

  2. Center for PBBEF Research, North Brunswick, New Jersey, USA

    John C. Lee

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Xiao, Z., Guo, H., Lam, M.S. (2015). Quantile Regression and Value at Risk. In: Lee, CF., Lee, J. (eds) Handbook of Financial Econometrics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7750-1_41

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  • DOI: https://doi.org/10.1007/978-1-4614-7750-1_41

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-7749-5

  • Online ISBN: 978-1-4614-7750-1

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