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Evaluating Value-at-Risk models via Quantile Regression

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  • Wagner Piazza Gaglianone

    ()

  • Luiz Renato Lima

    ()

  • Oliver Linton

    ()

  • Daniel Smith

    ()

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 Christoffersen (1998) and Engle and Maganelli (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 condition to assess the finite sample performance of a quantile model whereas the existing ones do not. The proposed methodology allows us to identify periods of an increased risk exposure based on a quantile regression model (Koenker & 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 Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we094625.

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Date of creation: May 2009
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Handle: RePEc:cte:werepe:we094625

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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. Cathy W. S. Chen & Richard Gerlach & Bruce B. K. Hwang & Michael McAleer, 2011. "Forecasting Value-at-Risk Using Nonlinear Regression Quantiles and the Intra-day Range," KIER Working Papers 775, Kyoto University, Institute of Economic Research.
  2. Sirio Aramonte & Marius del Giudice Rodriguez & Jason J. Wu, 2011. "Dynamic factor value-at-risk for large, heteroskedastic portfolios," Finance and Economics Discussion Series 2011-19, Board of Governors of the Federal Reserve System (U.S.).
  3. 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.
  4. Elena-Ivona Dumitrescu & Christophe Hurlin & Vinson Pham, 2012. "Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests," Working Papers halshs-00671658, HAL.
  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. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Feb 2014.
  7. 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.
  8. 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.
  9. 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.

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