Capturing dependence among large losses using extreme‐value copulas: Impacts on capital requirements for (re)insurers in regulated markets

What the paper says

Abstract Certain events can trigger multiple insurance claims across different lines of business (LOB), requiring insurers to pay out several indemnities simultaneously. Examples include car accidents causing both vehicle damage, third‐party liability, and personal injury, or natural disasters generating widespread losses. Solvency capital requirements (SCR) should account for the dependence of such claims, rather than treating them in isolation. In this study, we employ extreme‐value copulas (EVC) to model the dependence structure of claims arising from single events across multiple LOBs within a real insurance company. We assess how this dependence influences capital requirements. Our results show that EVC outperforms elliptical and Archimedean copulas in capturing tail dependencies when evaluating LOB‐specific Value‐at‐Risk (VaR). However, since insurers must absorb total aggregated losses, capital adequacy should reflect aggregation risk. In such cases, radially symmetric copulas (e.g., t‐Copula or Frank) may be more appropriate. A review of SCR models used in Brazil, Europe, and the US reveals that existing frameworks tend to overestimate required capital and may be insufficient for extreme‐event scenarios. The study contributes to the literature by showing the benefits of incorporating EVC into solvency modeling, and by identifying limitations in current regulatory approaches, as the procedure used to estimate tail dependence (the “data‐cutting method”). We also recommend the development of internal models tailored to the specific risk profile of each insurer, promoting both financial resilience and competitive advantage.