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Evaluating Value-at-Risk Models via Quantile Regression

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Author Info

  • Wagner Piazza Gaglianone

    ()
    (Central Bank of Brazil and Fucape Buisness School)

  • Luiz Renato Lima

    ()
    (University of Tennessee and EFGE-FGV)

  • Oliver Linton

    ()
    (London School of Economics)

  • Daniel Smith

    ()
    (Simon Fraser University and QUT)

Abstract

This paper is concerned with evaluating Value-at-Risk estimates. It is well known that using only binary variables, such as whether or not there was an exception, sacrifices too much information. However, most of the specification tests (also called backtests) available in the literature, such as Christofferson (1998) and Engle and Mangenelli (2004) are based on such variables. In this paper we propose a new backtest that does not rely solely on binary variables. It is shown that the new backtest provides a sufficient condtion to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodolgy allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker and Xiao, 2002). Our theoretical findings are corroborated through a Monte Carlo simulation and an empirical exercise with daily S&P500 time series.

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Bibliographic Info

Paper provided by National Centre for Econometric Research in its series NCER Working Paper Series with number 67.

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Length: 27 pages
Date of creation: 05 Nov 2010
Date of revision:
Publication status: forthcoming
Handle: RePEc:qut:auncer:2010_14

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Keywords: Value-at-Risk; Backtesting; Quantile Regression;

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References

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Citations

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Cited by:
  1. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Feb 2014.
  2. Chen, C.W.S. & Gerlach, R. & Hwang, B.B.K. & McAleer, M.J., 2011. "Forecasting Value-at-Risk Using Nonlinear Regression Quantiles and the Intraday Range," Econometric Institute Research Papers EI 2011-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Rubia, Antonio & Sanchis-Marco, Lidia, 2013. "On downside risk predictability through liquidity and trading activity: A dynamic quantile approach," International Journal of Forecasting, Elsevier, vol. 29(1), pages 202-219.
  4. Diego Fresoli & Esther Ruiz, 2014. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Statistics and Econometrics Working Papers ws140202, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. Colletaz, Gilbert & Hurlin, Christophe & Pérignon, Christophe, 2013. "The Risk Map: A new tool for validating risk models," Journal of Banking & Finance, Elsevier, vol. 37(10), pages 3843-3854.
  6. Elena-Ivona Dumitrescu & Christophe Hurlin & Vinson Pham, 2012. "Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests," Working Papers halshs-00671658, HAL.
  7. Wagner Piazza Gaglianone & Jaqueline Terra Moura Marins, 2014. "Risk Assessment of the Brazilian FX Rate," Working Papers Series 344, Central Bank of Brazil, Research Department.
  8. Aramonte, Sirio & Giudice Rodriguez, Marius del & Wu, Jason, 2013. "Dynamic factor Value-at-Risk for large heteroskedastic portfolios," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4299-4309.
  9. Hua, Jian & Manzan, Sebastiano, 2013. "Forecasting the return distribution using high-frequency volatility measures," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4381-4403.

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