Using Extreme Value Theory to Model Insurance Risk of Nigeria's Motor Industrial Class of Business

Abstract

Extreme losses have been recorded in Nigeria insurance companies due to motor insurance class claims; Nigeria Insurance market being a developing one requires building the confidence of the public to subscribe to their products. Nigeria’s motor industrial insurance claim data for five insurance companies in a two year period is modelled in this paper with extreme value theory (EVT) to estimate the Value-at-Risk (VaR), where VaR gives estimate of the minimum amount of claims an insurance company would pay in a given period of time. The time series plot was obtained which aimed at capturing the trend of the claims over the two-year period, the mean excess plot was obtained which helped to determine threshold and the shape of the distribution in the tail area. The returns were then fitted in a Generalized Pareto model (GPD), a similar model that would have been used is the Generalized Extreme Value model (GEV) but the GPD is used in this study because it describes what happens in the tail area of the distribution and not just the maximum tail. A linear Q-Q plot reveals that parametric model fits the data well. VaR estimate was finally obtained using the extreme value method and other two methods of Historical and Gaussian at 5% confidence interval. The three methods of estimating VaR were compared and the empirical result shows that extreme VaR is most suitable to calculate VaR as compared to the Historical and Gaussian method.