Optimal basis risk weighting in expectile-based parametric insurance

TL;DR

This paper investigates the optimal weighting of basis risk in expectile-based parametric insurance, addressing model uncertainty and providing theoretical and simulation insights into insurance design.

Contribution

It characterizes the existence and uniqueness of optimal basis risk weights within a utility-maximization framework and links distribution properties to expectile derivatives.

Findings

Established boundary conditions for optimal basis risk weights.

Compared utility outcomes of no insurance and full coverage.

Simulated hurricane insurance to analyze risk and premium effects.

Abstract

Parametric insurance contracts translate index measurements to compensation for policyholders' losses using predefined payment schemes. These need to be designed carefully to keep basis risk, i.e. the disparity between payouts and true damages, small. Previous research has motivated the use of conditional expectiles as payment schemes, whose compensation is impacted by the policyholder's potentially unknown attitude towards basis risk. To alleviate this model uncertainty and to investigate the impact of (hidden) influencing factors, we characterize existence and uniqueness of the optimal basis risk weighting in a utility-maximization framework through a set of boundary conditions. In the absence of an optimal solution, we provide comparisons to the utility of no insurance and full indemnity coverage. We establish a link between location-scale distributions and separability of conditional expectiles' derivatives, thus improving the understanding of these statistical functionals. A simulation study on parametric hurricane insurance visualizes our results, investigates the influence of premium loading and risk aversion on the optimal weighting, and comments on the challenge of (spatial) loss dependence.