Applying Copula Models to Correlated Insurance Risks in Nigerian Multi-Line Insurers

This study applies copula modelling techniques to quantify the dependence structure among correlated insurance risks in Nigerian multi-line insurance companies, contributing to improved aggregate loss distribution estimation and capital requirement calculations. Traditional aggregate loss models assume independence across insurance lines, which underestimates tail risk when claim shocks are positively correlated due to common economic, environmental, or catastrophic drivers. Copula models offer a flexible framework for modelling the joint distribution of losses across lines while separately specifying marginal distributions and dependence structures. This study uses aggregate claims data from five multi-line Nigerian insurers for the period 2016 to 2023, covering motor, property, marine, and liability lines. Marginal loss distributions are fitted separately for each line using maximum likelihood estimation. Gaussian, t-copula, Clayton, Gumbel, and Frank copula families are fitted to assess the dependence structure, with the best-fitting copula selected using AIC and BIC criteria. Aggregate VaR and TVaR are computed and compared against independence-assumption estimates. Findings reveal significant positive dependence among motor, property, and liability lines, with tail dependence best captured by the t-copula. Independence assumption estimates of aggregate 99.5 percent VaR understate the copula-based estimate by an average of 23 percent. The study concludes that copula modelling materially improves the accuracy of aggregate risk quantification for Nigerian multi-line insurers. It recommends that NAICOM incorporate dependence modelling requirements into its evolving risk-based capital framework.

Keywords: copula models, correlated risks, multi-line insurance, aggregate loss, capital requirements.