Optimum Hurricane Futures Hedge in a Warming Environment: A Risk–Return Jump‐Diffusion Approach

ABSTRACT We develop an optimum risk-return hurricane hedge model in a doubly stochastic jump-diffusion economy. The model's concave risk-return tradeoff dictates that a higher correlation between hurricane power and insurer's loss, a smaller variable hedging cost, and a larger market risk premium result in a less costly but more effective hedge. The resulting hedge ratio comprises of a positive diffusion, a positive jump, and a negative hedging cost component. Numerical results show that hedging hurricane jump risks is most crucial with jump volatility being the dominant factor, and the faster the warming the more pronounced the jump effects. INTRODUCTION Economic losses from climate change are substantial and on the rise. (1) The risk of property damage and loss from hurricanes has been progressively magnified by the ongoing growth of coastal population and property values. (2) Scientific evidence (3) further finds that an increasing level of greenhouse gas concentrations would lead to increased severity and frequency of tropical cyclones. These bleak projections, combined with the limited capacity of the insurance industry due to regulations, transaction costs, and geographic concentration of insured risk, subject insurers to facing a new era of climate risks management needing new hedging strategies. Traditionally, insurance companies seek protection against underwriting risk through the mechanism of reinsurance, but worldwide capacity shortage coupled with the rising number of catastrophes in recent years have made securitization of catastrophic losses on both exchanges and over-the-counter markets a timely and desirable functional alternative. A number of catastrope (CAT)-linked instruments, such as Hurricane Risk Landfall Options (HuRLOs) launched by Weather Risk Solutions in 2008, Hurricane CAT Bonds (e.g., one launched by USAA Inc. in 1997), Hurricane CatEPuts, and the exchange-traded Hurricane Futures and Futures Options have been developed as a result. Among them, the exchange-traded hurricane futures market took off after the 2004-2005 storms saddled the insurance industry. For insurance companies, hurricane futures can provide additional coverage even if they have already bought traditional backup insurance. Similarly, banks, utilities, energy companies, state governments, and pension funds have strong motivations to seek additional coverage if a massive hurricane or a series of storms make landfall in their region. One of the important issues in futures hedging is the variables considered in the objective function of the optimization problem. The traditional risk-minimization futures hedging approach developed by Johnson (1960) and Edrington (1979) formulates optimum futures hedge by assuming a diffusion underlying process, and then minimizing the one-period risk of the hedge portfolio using the least square regression or its variations. (4) Corporate hedging literature has, however, consistently found that actual hedge ratios for commodity firms are significantly lower than those prescribed under the risk-minimization approach, because while making a hedging decision, firms consider not only risk minimization but also the hedging costs incurred. These hedging costs comprise of the fixed cost of setting up and maintaining a hedge program and the variable costs from the forgone expected return and from servicing portfolio rebalancing and daily resettlements. (5) These findings suggest an optimal futures hedge model to be set in a risk-return trade-off framework. Another critical issue in hedging using weather derivatives lies in the specification of physical weather and climate processes. Unlike the norm in perfectly functioning and complete financial markets where the no-arbitrage condition prevails and processes can be random, such as the common assumption of a diffusion underlying process in the traditional risk-minimization hedging models, climate processes are set in missing and incomplete markets such that their characteristic structure need be included in the pricing models. …