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Systematic stress tests with entropic plausibility constraints


  • Breuer, Thomas
  • Csiszár, Imre


Stress tests with handpicked scenarios might misrepresent risks either because dangerous scenarios are not considered or because the scenarios considered are too implausible. To overcome these two pitfalls we propose a systematic search for the worst case within a relative entropy ball of sufficiently plausible scenarios. For this purpose we use mixed scenarios, which are risk factor distributions rather than realisations. A Maximum Loss theorem explicitly gives the worst case distribution. The method is illustrated in a number of example applications: linear and quadratic portfolios, stressed default probabilities, stressed correlations, macroeconomic stress tests.

Suggested Citation

  • Breuer, Thomas & Csiszár, Imre, 2013. "Systematic stress tests with entropic plausibility constraints," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1552-1559.
  • Handle: RePEc:eee:jbfina:v:37:y:2013:i:5:p:1552-1559 DOI: 10.1016/j.jbankfin.2012.04.013

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    References listed on IDEAS

    1. M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
    2. Thomas Breuer & Martin Jandacka & Klaus Rheinberger & Martin Summer, 2009. "How to Find Plausible, Severe and Useful Stress Scenarios," International Journal of Central Banking, International Journal of Central Banking, vol. 5(3), pages 205-224, September.
    3. Paul Louis Ceriel Hilbers & Matthew T Jones & Graham L Slack, 2004. "Stress Testing Financial Systems; What to Do When the Governor Calls," IMF Working Papers 04/127, International Monetary Fund.
    4. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    5. Maria Soledad Martinez Peria & Giovanni Majnoni & Matthew T Jones & Winfrid Blaschke, 2001. "Stress Testing of Financial Systems; An Overview of Issues, Methodologies, and FSAP Experiences," IMF Working Papers 01/88, International Monetary Fund.
    6. Breuer, Thomas & Jandačka, Martin & Mencía, Javier & Summer, Martin, 2012. "A systematic approach to multi-period stress testing of portfolio credit risk," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 332-340.
    7. Barillas, Francisco & Hansen, Lars Peter & Sargent, Thomas J., 2009. "Doubts or variability?," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2388-2418, November.
    8. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 21-52.
    9. Marco Sorge, 2004. "Stress-testing financial systems: an overview of current methodologies," BIS Working Papers 165, Bank for International Settlements.
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    Cited by:

    1. Pierluigi Bologna & Anatoli Segura, 2016. "Integrating stress tests within the Basel III capital framework: a macroprudentially coherent approach," Questioni di Economia e Finanza (Occasional Papers) 360, Bank of Italy, Economic Research and International Relations Area.
    2. repec:eee:matcom:v:143:y:2018:i:c:p:89-98 is not listed on IDEAS
    3. 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.
    4. repec:rfa:aefjnl:v:4:y:2017:i:3:p:155-163 is not listed on IDEAS
    5. Andrew McKenna & Rhys Bidder, 2014. "Robust Stress Testing," 2014 Meeting Papers 853, Society for Economic Dynamics.
    6. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    7. repec:eee:ejores:v:264:y:2018:i:2:p:707-716 is not listed on IDEAS
    8. repec:eee:apmaco:v:274:y:2016:i:c:p:495-518 is not listed on IDEAS
    9. De Genaro, Alan, 2016. "Systematic multi-period stress scenarios with an application to CCP risk management," Journal of Banking & Finance, Elsevier, vol. 67(C), pages 119-134.
    10. repec:spr:annopr:v:260:y:2018:i:1:d:10.1007_s10479-016-2284-3 is not listed on IDEAS
    11. Mokinski, Frieder, 2017. "A severity function approach to scenario selection," Discussion Papers 34/2017, Deutsche Bundesbank.

    More about this item


    Scenario analysis; Worst case; Risk measures; Multiple priors; Model risk; Relative entropy;

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G01 - Financial Economics - - General - - - Financial Crises
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • M48 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Government Policy and Regulation


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