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Robust measurement of (heavy-tailed) risks: Theory and implementation


  • Schneider, Judith C.
  • Schweizer, Nikolaus


Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case. Moreover, we present a novel, empirical way built on model confidence sets (MCS) for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. We demonstrate the implications of heavy-tailed risks for the choice of the divergence measure and the empirical divergence estimation. For heavy-tailed risks, the simulation of the worst-case distribution is numerically intricate. We present a Sequential Monte Carlo algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach.

Suggested Citation

  • Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.
  • Handle: RePEc:eee:dyncon:v:61:y:2015:i:c:p:183-203
    DOI: 10.1016/j.jedc.2015.09.010

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    Cited by:

    1. repec:bla:jrinsu:v:84:y:2017:i:s1:p:459-475 is not listed on IDEAS
    2. Li, Jing, 2018. "Essays on model uncertainty in financial models," Other publications TiSEM 202cd910-7ef1-4db4-94ae-d, Tilburg University, School of Economics and Management.
    3. Thomas Kruse & Judith C. Schneider & Nikolaus Schweizer, 2015. "What's in a ball? Constructing and characterizing uncertainty sets," Papers 1510.01675,

    More about this item


    Divergence estimation; Model risk; Risk management; Robustness; Sequential Monte Carlo;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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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