Explicit Diversification Beneift for Dependent Risks

SCOR papers, No. 38, 2016

27 Pages Posted: 18 Apr 2016

See all articles by Michel M. Dacorogna

Michel M. Dacorogna

PRS Solutions

Laila Elbahtouri

SCOR

Marie Kratz

ESSEC Business School, CREAR risk research center

Date Written: April 15, 2016

Abstract

We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence.

Keywords: Aggregation of risks, Archimedean copula, Clayton, Diversification (benefit), Gaussian, Gumbel, Heavy tail, Mixing technique, Pareto, Risk measure, TVaR, VaR, Weibull

JEL Classification: C00, C13, C15

Suggested Citation

Dacorogna, Michel M. and Elbahtouri, Laila and Kratz, Marie, Explicit Diversification Beneift for Dependent Risks (April 15, 2016). SCOR papers, No. 38, 2016, Available at SSRN: https://ssrn.com/abstract=2765403 or http://dx.doi.org/10.2139/ssrn.2765403

Michel M. Dacorogna (Contact Author)

PRS Solutions ( email )

Raingässli 1
Zug, Zug 6300
Switzerland

Laila Elbahtouri

SCOR ( email )

92074 Paris La Defense Cedex
France

Marie Kratz

ESSEC Business School, CREAR risk research center ( email )

Avenue Bernard Hirsch
BP 50105
CERGY PONTOISE CEDEX 95021
France

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