Modeling Insurance Returns with Extreme Value Theory (A Case Study for Kenya’s Fire Industrial Insurance Class of Business).

Abstract

Most General insurance companies have faced huge losses arising from fire industrial class of business .It is for this reason this study uses extreme value theory approach to model these returns. Traditionally normal distribution was applied and could not capture rare events which caused enormous losses. Kenya’s Fire industrial insurance data for five insurance companies and average for entire industry was read into R program .The objective was to plot the time series data.  The time series plots aimed to capture the trend and the behavior of the returns over a seven year period. The returns were then standardized in order to transform the negative returns. Using fExtremes in R, the mean excess plot was obtained which helped in measuring the shape of the distribution in the tail. The returns were fitted in a GPD Model in which the excess distribution and the tail of the underlying distribution were obtained over a chosen threshold. These were significant in capturing the values that exceeded the threshold. They were found to be a smooth curve which implied the GPD fit was a good for the data. Scatter plot was obtained and a solid line was observed in the scatter plot which was the smooth of the scattered residuals. QQ plots were also obtained and followed linear form which implied that the parametric model fitted the data well. VaR estimate was finally obtained using extreme value method. The log log empirical distribution was also obtained and indicated how the data points were distributed. After the excesses over a high threshold were fitted to the GPD, parameters were estimated which were used to estimate VaR at different confidence intervals.

Key words: Extreme Value Theory, Peak Over Threshold, Generalized Pareto Distribution, Value at Risk.