A Closed-Form Formula for the Skewness Estimation of Non-Life Reserve Risk Distribution

Abstract

In the same spirit as the Mack standard deviation for non-life reserves, which can be estimated with a closed-form formula applied to a loss development triangle (see Mack 1993), this article introduces a closed-form formula to estimate the skewness of non-life reserves which can also be applied to a loss development triangle. This closed-form formula is tested on 41 triangles and estimators of skewness per different lines of business are derived. These estimators are used to calibrate skew-normal and Generalized Extreme Value ("GEV") distributions for a fictitious reinsurance company so that a capital amount related to the reserve risk of this company using an internal model is calculated. This capital amount is then compared to the capital amount which would result from the use of lognormal distributions instead of skew-normal or GEV distributions. An excel sheet developed to estimate the presented closed-form formula is available on the internet.