Flexible Weather Index Insurance Design with Penalized Splines

Abstract

In this paper we propose a flexible framework for the design of weather index insurance (WII) based on penalized spline methods. The aim is to find the indemnity function which optimally characterizes the intricate relationship between agricultural production losses and weather variables and thus effectively improves policyholders’ utilities. We use B-spline functions to define the feasible set of the optimization problem and a penalty function to avoid the “overfitting” issue. The proposed design framework is applied to an empirical study in which we use precipitation and vapor pressure deficit (VPD) to construct an index insurance contract for corn producers in Illinois. Numerical evidence shows that the resulting optimal insurance contract effectively enhances policyholder’s utility, even in the absence of government’s premium subsidy. In addition, performance of our proposed index insurance is robust to a variety of key factors, and the general payment structure is highly interpretable for marketing purposes. All these merits indicate its potential to increase efficiency of the agricultural insurance market and thus enhance social welfare.

Keywords: Weather index insurance, basis risk, insurance design, spline