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Economic Capital Management For Insurance Companies Using Conditional Value At Risk And A Copula Approach


  • Rossella Bisignani

    () (Univerity of Rome "La Sapienza")

  • Giovanni Masala

    () (University of Cagliari)

  • Marco Micocci

    () (University of Cagliari)


The loss ratio (LR) for insurance companies is defined as the ratio of incurred claims and earned premiums for a specified class of insurance (CoI). The company may estimate then its capital requirement for that particular CoI by using Value at Risk (VaR) or conditional VaR (CVaR) of the loss ratio distribution at a specified probability value. The overall objective of the company is to evaluate the aggregate capital requirement through a weighted sum of marginal capital requirements for all the classes of insurance. Nevertheless, this procedure may tend to over-estimate the aggregate capital requirement because it does not take into consideration the real dependence amongst the different classes of insurance. In other words, perfect dependence does not allow considering diversification effects. In this paper, we present a model which permits to take into consideration real correlations of the several CoIs. Thanks to copula functions, we are able to generate (by Monte Carlo simulations) correlated loss ratios with known marginal distributions. This approach is described through a numerical example that used data collected from some of the most important Italian non life insurance companies. We show then the diversification benefit thus obtained. We conclude the paper building an efficient frontier on the plane LR - CVaR; the efficient frontier may be considered a useful tool to manage the global company risk.

Suggested Citation

  • Rossella Bisignani & Giovanni Masala & Marco Micocci, 2006. "Economic Capital Management For Insurance Companies Using Conditional Value At Risk And A Copula Approach," Economia, Societa', e Istituzioni, Dipartimento di Economia e Finanza, LUISS Guido Carli, vol. 0(3).
  • Handle: RePEc:lui:rivesi:1832

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    References listed on IDEAS

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    More about this item


    non life insurance; loss ratio; copula functions; capital requirement; Monte Carlo simulation; risk measures; efficient frontier.;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation


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