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VAR for VaR: measuring systemic risk using multivariate regression quantiles

Author

Listed:
  • White, Halbert
  • Kim, Tae-Hwan
  • Manganelli, Simone

Abstract

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market returns data to analyse spillovers in the values at risk (VaR) of different financial institutions. We construct impulse-response functions for the quantile processes of a sample of 230 financial institutions around the world and study how financial institution-specific and system-wide shocks are absorbed by the system.

Suggested Citation

  • White, Halbert & Kim, Tae-Hwan & Manganelli, Simone, 2010. "VAR for VaR: measuring systemic risk using multivariate regression quantiles," MPRA Paper 35372, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:35372
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    File URL: https://mpra.ub.uni-muenchen.de/35372/1/MPRA_paper_35372.pdf
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    References listed on IDEAS

    as
    1. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    2. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(03), pages 295-317, September.
    3. Viral V. Acharya & Lasse H. Pedersen & Thomas Philippon & Matthew Richardson, 2010. "Measuring systemic risk," Working Paper 1002, Federal Reserve Bank of Cleveland.
    4. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, March.
    5. Manganelli, Simone & White, Halbert & Kim, Tae-Hwan, 2008. "Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR," Working Paper Series 957, European Central Bank.
    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. repec:cep:stiecm:/2014/574 is not listed on IDEAS
    8. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
    9. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    10. Karun Adusumilli & Taisuke Otsu, 2017. "Empirical Likelihood for Random Sets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1064-1075, July.
    11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    12. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    13. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(01), pages 46-68, March.
    14. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
    15. Komunjer, Ivana & Vuong, Quang, 2010. "Efficient estimation in dynamic conditional quantile models," Journal of Econometrics, Elsevier, vol. 157(2), pages 272-285, August.
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    Citations

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    Cited by:

    1. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, Elsevier.
    2. Hautsch, Nikolaus & Schaumburg, Julia & Schienle, Melanie, 2014. "Forecasting systemic impact in financial networks," International Journal of Forecasting, Elsevier, vol. 30(3), pages 781-794.
    3. Castro, Carlos & Ferrari, Stijn, 2014. "Measuring and testing for the systemically important financial institutions," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 1-14.
    4. Giovanni Bonaccolto & Massimiliano Caporin, 2016. "The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 9(3), pages 1-25, July.
    5. Raffaella Calabrese & Silvia Osmetti, 2014. "Modelling cross-border systemic risk in the European banking sector: a copula approach," Papers 1411.1348, arXiv.org.

    More about this item

    Keywords

    Quantile impulse-responses; spillover; codependence; CAViaR;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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