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Copulas can be a useful tool to capture heavy-tailed dependence between risks in estimating economic capital. This paper provides a procedure of combining copula with GARCH model to construct a multivariate distribution. The copula-based GARCH model using a skewed student’s t-distribution controls for the issues of skewness, heavy tails, volatility clustering and conditional dependencies contained in the financial time series data. Using the sample of U.S. property liability insurance industry, we perform Monte Carlo simulation to estimate the insurer’s economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). The result indicates that the choice of dependence structure and business mix between asset classes and liability lines has a significant impact on the resulting capital requirements and diversification benefits. We find the incremental diversification benefit in terms of a reduction in the total capital requirement from the joint modeling of underwriting risk and market risk compared to the modeling of market risk only.

Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model