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Evaluating Value-at-Risk Models via Quantile Regression

  • 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)

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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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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  2. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
  3. Sean D. Campbell, 2005. "A review of backtesting and backtesting procedures," Finance and Economics Discussion Series 2005-21, Board of Governors of the Federal Reserve System (U.S.).
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  5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  6. Issler, João Victor & Lima, Luiz Renato Regis de Oliveira, 2007. "A Panel Data Approach to Economic Forecasting: The Bias-Corrected Average Forecast," Economics Working Papers (Ensaios Economicos da EPGE) 642, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
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  17. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
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