Moral Hazard, Basis Risk, and Gap Insurance

Abstract

This article addresses the trade-off between moral hazard and basis risk. A decision maker, e.g., a primary insurer, is considered who can purchase an index hedge and a (re)insurance contract that covers the gap between actual losses and the index-linked payout, or part of this gap. The results suggest that combining insurance with an index hedge may extend the possibility set and by that means lead to efficiency gains. Naturally, the results depend heavily on the transaction costs associated with both instruments. In particular, the authors show that if the index product is without transaction costs, at least some index-linked coverage is always purchased, so long as there is positive correlation between the index and the actual losses. So under these circumstances, there is in any case a benefit from the availability of index products. Furthermore, it is shown that the index hedge would always be supplemented by a positive amount of gap insurance.