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Validation of aggregated risks models

Published online by Cambridge University Press:  04 December 2017

Michel Dacorogna ,
Laila Elbahtouri  and
Marie Kratz
Michel Dacorogna
Affiliation:
DEAR-Consulting, Scheuchzerstrasse 160, 8057 Zurich, Switzerland
Laila Elbahtouri
Affiliation:
SCOR, 5 Avenue Kléber, 75795 Paris, France
Marie Kratz*
Affiliation:
ESSEC Business School, CREAR Risk Research Center, Avenue Bernard Hirsch, BP50105, 95021 Cergy-Pontoise, France
*
*Correspondence to: ESSEC Business School, CREAR Risk Research Center, Avenue Bernard Hirsch, BP50105, 95021 Cergy-Pontoise, France. E-mail: kratz@essec.edu
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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.

Keywords

Diversification (benefit)Heavy tailMixing techniqueModel validationMonte-Carlo simulation
Type
Paper
Information
Annals of Actuarial Science , Volume 12 , Issue 2 , September 2018 , pp. 433 - 454
Copyright
© Institute and Faculty of Actuaries 2017 

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