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The Risk Map: A New Tool for Validating Risk Models

Author

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  • Gilbert Colletaz

    () (LEO - Laboratoire d'économie d'Orleans - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Hurlin

    () (LEO - Laboratoire d'économie d'Orleans - UO - Université d'Orléans - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Pérignon

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. It relies on the concept of a super exception, which is de.ned as a situation in which the loss exceeds both the standard Value-at-Risk (VaR) and a VaR de.ned at an extremely low coverage probability. We then formally test whether the sequences of exceptions and super exceptions are rejected by standard model validation tests. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.

Suggested Citation

  • Gilbert Colletaz & Christophe Hurlin & Christophe Pérignon, 2012. "The Risk Map: A New Tool for Validating Risk Models," Working Papers halshs-00746273, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00746273
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00746273
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    as
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    Cited by:

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    2. Sharif Mozumder & Arafatur Rahman, 2016. "Market Risk Of Investment In Us Subprime Crisis: Comparison Of A Pure Diffusion And A Pure Jump Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 1-17, September.
    3. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    4. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    5. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
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    7. Jean-Edouard Colliard, 2019. "Strategic Selection of Risk Models and Bank Capital Regulation," Management Science, INFORMS, vol. 67(6), pages 2591-2606, June.
    8. Hamid, Alain & Heiden, Moritz, 2015. "Forecasting volatility with empirical similarity and Google Trends," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 62-81.
    9. Marta Małecka, 2021. "Testing for a serial correlation in VaR failures through the exponential autoregressive conditional duration model," Statistics in Transition New Series, Polish Statistical Association, vol. 22(1), pages 145-162, March.
    10. Bujaki, Merridee & Lento, Camillo & Sayed, Naqi, 2019. "Utilizing professional accounting concepts to understand and respond to academic dishonesty in accounting programs," Journal of Accounting Education, Elsevier, vol. 47(C), pages 28-47.
    11. Sylvain Benoît & Gilbert Colletaz & Christophe Hurlin & Christophe Pérignon, 2013. "A Theoretical and Empirical Comparison of Systemic Risk Measures," Working Papers halshs-00746272, HAL.
    12. Kratz, Marie & Lok, Yen H. & McNeil, Alexander J., 2018. "Multinomial VaR backtests: A simple implicit approach to backtesting expected shortfall," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 393-407.
    13. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    14. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    15. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    16. Manner, Hans & Alavi Fard, Farzad & Pourkhanali, Armin & Tafakori, Laleh, 2019. "Forecasting the joint distribution of Australian electricity prices using dynamic vine copulae," Energy Economics, Elsevier, vol. 78(C), pages 143-164.
    17. Tsukahara, Fábio Yasuhiro & Kimura, Herbert & Sobreiro, Vinicius Amorim & Zambrano, Juan Carlos Arismendi, 2016. "Validation of default probability models: A stress testing approach," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 70-85.
    18. Laura Garcia-Jorcano & Alfonso Novales, 2020. "A dominance approach for comparing the performance of VaR forecasting models," Computational Statistics, Springer, vol. 35(3), pages 1411-1448, September.
    19. Argyropoulos, Christos & Panopoulou, Ekaterini, 2019. "Backtesting VaR and ES under the magnifying glass," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 22-37.
    20. Laura Garcia-Jorcano & Alfonso Novales, 0. "A dominance approach for comparing the performance of VaR forecasting models," Computational Statistics, Springer, vol. 0, pages 1-38.
    21. Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.

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    More about this item

    Keywords

    Financial Risk Management; Tail Risk; Basel III;
    All these keywords.

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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