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Validation of aggregated risks models

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  • Dacorogna, Michel
  • Elbahtouri, Laila
  • Kratz, Marie

Abstract

Validation of risk models is required by regulators and demanded by management and shareholders. Those models rely in practice heavily on Monte Carlo (MC) simulations. Given their complexity, the convergence of the MC algorithm is difficult to prove mathematically. To circumvent this problem and nevertheless explore the conditions of convergence, we suggest an analytical approach. Considering standard models, we compute, via mixing techniques, closed form formulas for risk measures as Value-at-Risk (VaR) VaR or Tail Value-at-Risk (TVaR) TVaR on a portfolio of risks, and consequently for the associated diversification benefit. The numerical convergence of MC simulations of those various quantities is then tested against their analytical evaluations. The speed of convergence appears to depend on the fatness of the tail of the marginal distributions; the higher the tail index, the faster the convergence. We also explore the behaviour of the diversification benefit with various dependence structures and marginals (heavy and light tails). As expected, it varies heavily with the type of dependence between aggregated risks. The diversification benefit is also studied as a function of the risk measure, VaR or TVaR.

Suggested Citation

  • Dacorogna, Michel & Elbahtouri, Laila & Kratz, Marie, 2018. "Validation of aggregated risks models," Annals of Actuarial Science, Cambridge University Press, vol. 12(2), pages 433-454, September.
  • Handle: RePEc:cup:anacsi:v:12:y:2018:i:02:p:433-454_00
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    Cited by:

    1. Michel Dacorogna, 2023. "How to Gain Confidence in the Results of Internal Risk Models? Approaches and Techniques for Validation," Risks, MDPI, vol. 11(5), pages 1-20, May.
    2. Bingzhen Geng & Yang Liu & Yimiao Zhao, 2024. "Value-at-Risk- and Expectile-based Systemic Risk Measures and Second-order Asymptotics: With Applications to Diversification," Papers 2404.18029, arXiv.org.

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