Analyzing solvency with extreme value theory: an application to the Spanish motor liability insurance market

Abstract

An accurate estimation of extreme claims is fundamental to assess solvency capital requirements (SCR) established by Solvency II. Basing on the Extreme Value Theory (EVT), this paper performs a parametric estimation to fit the motor liability insurance historical datasets of two significant and representative companies operating within the Spanish market to a Generalized Pareto Distribution. We illustrate how EVT improves classical adjustments, as it considers outliers apart from mass risks, what leads to optimize the pricing decision-making and fix a risk transfer position.

Keywords

• Generalized Pareto Distribution
• Tail estimation
• Solvency II
• excesses over high thresholds
• Solvency capital requirements
• XL Reinsurance
• risk measures