Expectiles as basis risk-optimal payment schemes in parametric insurance

Payments in parametric insurance solutions are linked to an index and thus decoupled from policyholders' true losses. While this principle has appealing operational benefits compared to traditional indemnity coverage, i.e. is very efficient and cost effective, a downside is the discrepancy between payouts and actual damage, called basis risk. We show that in an asymmetrically weighted mean square error framework, the basis risk-minimizing payment schemes for pure parametric and parametric index insurance contracts can be expressed as conditional expectiles of policyholders' true loss given a compensation-triggering incident. We provide connections to stochastic orderings and demonstrate that regression approaches allow easy implementation in practice. Our results are visualized in parametric coverage for cyber risks and agricultural insurance.