The Effectiveness of Gap Insurance with Respect to Basis Risk in a Shareholder Value Maximization Setting

The purchase of index-linked alternative risk transfer instruments can lead to basis risk, if the insurer's loss is not fully dependent on the index. One way to reduce basis risk is to additionally purchase gap insurance, which fills the gap between an insurer's actual loss and the index-linked instrument's payout. Previous literature detects efficiency gains of this hedging strategy in a mean-variance framework. The aim of this paper is to extend this analysis and to examine the effectiveness of gap insurance in a shareholder value maximization framework under solvency constraints using differential evolution to solve the optimization problem. Our results show that purchasing gap insurance generally increases the hedging effectiveness in multiple ways by reducing basis risk, thus increasing the shareholder value and, at the same time, lowering the shortfall risk