Modeling underwriting risk: A copula regression analysis on U.S. property-casualty insurance byline loss ratios

Abstract

This article evaluates underwriting risks for U.S. property-casualty insurance company using a by-line multivariate framework. We propose a regression system with copula structure to estimate the dynamics and dependences of by-line loss ratio changes. The dynamics are characterized by autoregressive, macroeconomic, and line-specific variables. The dependences are characterized by symmetric, asymmetric, and vine copulas to manifest the contemporaneous risk. Both positive and negative dependence of loss ratio changes are found, and the lines of business contribute distinct diversification effects from the Risk-based Capital (RBC) R5 formula suggested. Based on empirical studies of industry-wide data, we confirm that the choice of copula structure and marginal estimation method affects the model's performance in the stress testing of catastrophic events. The proposed approach can be regarded as an internal model calculating the diversification benefits across business lines, based on a statistical hypothesis in contrast to a regulatory base. These findings help insurers and regulators to evaluate their capital requirements more precisely and reduce liability-side risk.