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Tile test for back-testing risk evaluation

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  • Gilles Zumbach

Abstract

A new test for measuring the accuracy of financial market risk estimations is introduced. It is based on the probability integral transform (PIT) of the ex post realized returns using the ex ante probability distributions underlying the risk estimation. If the forecast is correct, the result of the PIT, that we called probtile, should be an iid random variable with a uniform distribution. The new test measures the variance of the number of probtiles in a tiling over the whole sample. Using different tilings allow to check the dynamic and the distributional aspect of risk methodologies. The new test is very powerful, and new benchmarks need to be introduced to take into account subtle mean reversion effects induced by some risk estimations. The test is applied on 2 data sets for risk horizons of 1 and 10 days. The results show unambiguously the importance of capturing correctly the dynamic of the financial market, and exclude some broadly used risk methodologies.

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  • Gilles Zumbach, 2020. "Tile test for back-testing risk evaluation," Papers 2007.12431, arXiv.org.
    • Handle: RePEc:arx:papers:2007.12431
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    1. Fajardo, J. & Farias, A. R & Ornelas, J. R. H, 2003. "Goodness-of-fit Tests focus on VaR Estimation," Finance Lab Working Papers flwp_55, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    2. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    3. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    4. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
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