The Influence of Non-Linear Dependencies on the Basis Risk of Industry Loss Warranties

Index-linked catastrophic loss instruments represent an alternative to traditional reinsurance to hedge against catastrophic losses. The use of these instruments comes with benefits, such as a reduction of moral hazard and higher transparency. However, at the same time, it introduces basis risk as a crucial key risk factor, since the index and the company's losses are usually not fully dependent. The aim of this paper is to examine the impact of basis-risk on an insurer's solvency situation when an industry-loss-warranty contract is used for hedging. Since previous literature has consistently stressed the importance of a high degree of dependence between the company's losses and the industry index, we extend previous studies by allowing for non-linear dependencies between relevant processes (high-risk and low-risk assets, insurance company's loss and industry index). The analysis shows that both the type and degree of dependence play a considerable role with regard to basis-risk and solvency capital requirements and that other factors, such as relevant contract parameters of index-linked catastrophic loss instruments, should not be neglected to obtain a comprehensive and holistic view of their effect upon risk reduction