APPLICATION OF PEAK OVER THRESHOLD METHOD FOR VALUE AT RISK ESTIMATION IN PROPERTY INSURANCE

Abstract

Insurance companies, as providers of financial protection services, must manage risks accurately to avoid misestimating potential losses that could jeopardize financial stability. The magnitude of potential loss incurred by the insurer due to policyholder claims is commonly referred to as claim severity. A widely used risk measurement tool is Value at Risk (VaR), which estimates the maximum potential loss under the assumption of normally distributed data. However, in reality, claim amounts often exhibit extreme behavior very large values that occur with low frequency rendering conventional methods insufficient for accurate risk estimation. To address this, the present study employs Extreme Value Theory (EVT) with the Peak Over Threshold (POT) approach to model the distribution of extreme claim values. The POT method produces a Generalized Pareto Distribution (GPD), which effectively captures the heavy-tailed nature of the data. Extreme values are identified by selecting several candidate thresholds (u) using a mean excess function plot. The most appropriate threshold is then determined through the Kolmogorov–Smirnov test to ensure a good fit with the GPD. This optimal threshold is subsequently used to estimate the Value at Risk based on property insurance claim data from 2010 to 2016.