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Robustness and sensitivity analysis of risk measurement procedures

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  • Rama Cont

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, Center for Financial Engineering, Columbia University - Columbia University [New York])

  • Romain Deguest

    (Center for Financial Engineering, Columbia University - Columbia University [New York])

  • Giacomo Scandolo

    (DIMAD - Dipartimento di Matematica per le Decisioni - UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence)

Abstract

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ``risk measure" which summarizes the risk of the portfolio. We define the notion of ``risk measurement procedure", which includes both of these steps and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate in particular that using recently proposed risk measures like CVaR/ expected shortfall lead to a less robust risk measurement procedure than historical Value at Risk. We also propose alternative risk measurement procedures which possess the robustness property.

Suggested Citation

  • Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Post-Print hal-00413729, HAL.
    • Handle: RePEc:hal:journl:hal-00413729
    DOI: 10.1080/14697681003685597
    Note: View the original document on HAL open archive server: https://hal.science/hal-00413729v1
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