Measuring Economic Capital: Value-at-Risk, Expected Shortfall and Copula Approach

Abstract

It is important to incorporate diverse heavy-tailed dependency between risks in estimating economic capital. Copulas can be a useful technique to capture dependence structure where extreme events occur simultaneously. Using the sample of U.S. property liability insurance industry, we examine the impact of different dependence structure between market risk and underwriting risk of insurance portfolio on the economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). We identify the type of copula that best fits the given application data and perform a goodness of fit test to assess the adequacy of the copula model selected. The results suggest that the grouped t copula is better performed than the standard t copula to describe the dependence structure in an insurance setting where different type of risk factors coexists. The result also shows the incremental diversification benefit in the joint modeling of underwriting risk and market risk compared to the modeling of market risk only considered, indicating that both risks diversify against one another to some degree.