Probability modeling and estimation of risk measures for fire loss severity in pakistan: An application of extreme value theory

Abstract

Extreme events are increasing in the insurance and financial markets, causing large losses and ultimately huge insurance claims. Commercial fire loss severity has the largest value among the major insurance claims. The goal of our study is modeling the commercial fire loss severity and estimating the risk of extreme fire losses by using Extreme Value Theory (EVT). In the present study, we utilize the EVT (point over threshold modeling) for modeling the tail of fire loss data. We find that the Generalized Pareto distribution (GPD) gives more satisfactory fit to commercial fire loss data as compared to other parametric distributions including exponential, Pareto, gamma, logistic and generalized extreme value (GEV) distribution. In the empirical study, we determine the peaks over threshold of the GPD with the help of Mean Excess plots and Hill plots. We also estimate the risk measures like value at risk (VaR) and expected shortfall (ES). These estimates are helpful for pricing and risk management of non-insurance companies for their policy implications.