Extreme Value Theory and Catastrophe Loss Estimation for Nigerian Property Insurers

This study applies extreme value theory to estimate catastrophe loss distributions and probable maximum loss figures for Nigerian property insurance portfolios, addressing the limitations of traditional loss modelling approaches in characterizing extreme tail risk. Property insurance portfolios in Nigeria face exposure to infrequent but potentially catastrophic events including large urban fires, major floods, and industrial explosions, whose frequency and severity are best modelled by the heavy-tailed distributions that extreme value theory is specifically designed to handle. This study uses historical large property loss data from NAICOM industry loss statistics and individual company claims records from five property insurers for 2005 to 2023. Extreme value methods including the block maxima approach using the generalized extreme value distribution and the peaks over threshold approach using the generalized Pareto distribution are applied. Return level estimates at 50, 100, 200, and 500-year return periods are computed for urban fire, flood, and combined catastrophe scenarios. Findings reveal that the generalized Pareto distribution provides a significantly better fit to the tail of the Nigerian property loss distribution than lognormal or Pareto alternatives commonly used in practice. The 200-year probable maximum loss estimate exceeds the aggregate domestic reinsurance capacity for the property market by a factor of approximately 2.3. The study concludes that extreme value theory reveals catastrophe risk concentrations in the Nigerian property market that are inadequately covered by existing reinsurance arrangements. It recommends mandatory catastrophe scenario reporting for large property insurers.

Keywords: extreme value theory, catastrophe loss, probable maximum loss, property insurance, reinsurance.