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VAR for VaR: Measuring Tail Dependence Using Multivariate Regression Quantiles

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Author Info

  • Habert white
  • Tae-Hwan Kim

    (School of Economics, Yonsei University)

  • Simone Manganelli

    (European Central Bank, DG-Research)

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 equity returns data to analyse spillovers in the values at risk (VaR) between a market index and financial institutions. We construct impulse-response functions for the quantiles 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. We show how our methodology can successfully identify both in-sample and out-of-sample the set of financial institutions whose risk is most sentitive to market wide shocks in situations of financial distress, and can prove a valuable addition to the traditional toolkit of policy makers and supervisors.

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Bibliographic Info

Paper provided by Yonsei University, Yonsei Economics Research Institute in its series Working papers with number 2012rwp-45.

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Date of creation: Aug 2012
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Handle: RePEc:yon:wpaper:2012rwp-45

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Related research

Keywords: Quantile impulse-responses; spillover; codependence; CAViaR;

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References

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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  2. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
  3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  4. Acharya, Viral V & Pedersen, Lasse H & Philippon, Thomas & Richardson, Matthew P, 2012. "Measuring Systemic Risk," CEPR Discussion Papers 8824, C.E.P.R. Discussion Papers.
  5. P. Hartmann & S. Straetmans & C. G. de Vries, 2004. "Asset Market Linkages in Crisis Periods," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 313-326, February.
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  7. Karun Adusumilli & Taisuke Otsu, 2014. "Empirical Likelihood for Random Sets," STICERD - Econometrics Paper Series /2014/574, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
  9. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  10. 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.
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  12. 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.
  13. Viral V. Acharya, 2010. "Measuring systemic risk," Proceedings 1140, Federal Reserve Bank of Chicago.
  14. repec:fip:fedhpr:y:2010:i:may:p:65-71 is not listed on IDEAS
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Cited by:
  1. Hałaj, Grzegorz & Kok, Christoffer, 2013. "Assessing interbank contagion using simulated networks," Working Paper Series 1506, European Central Bank.
  2. Gross, Marco & Kok, Christoffer, 2013. "Measuring contagion potential among sovereigns and banks using a mixed-cross-section GVAR," Working Paper Series 1570, European Central Bank.
  3. Sylvain Benoit & Gilbert Colletaz & Christophe Hurlin & Christophe Pérignon, 2013. "A Theoretical and Empirical Comparison of Systemic Risk Measures," Working Papers halshs-00746272, HAL.
  4. Carlos Castro & Stijn Ferrari, 2011. "Measuring and testing for the systemically important financial institutions," DOCUMENTOS DE TRABAJO 008779, UNIVERSIDAD DEL ROSARIO.
  5. Markus K. Brunnermeier & Martin Oehmke, 2012. "Bubbles, Financial Crises, and Systemic Risk," NBER Working Papers 18398, National Bureau of Economic Research, Inc.
  6. di Mauro, Filippo & Fornari, Fabio & Mannucci, Dario, 2011. "Stock market firm-level information and real economic activity," Working Paper Series 1366, European Central Bank.

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