Reinsuring Climatic Risk Using Optimally Designed Weather Bonds

The aim of this paper is to determine the optimal structure of a weather bond, i.e. a bond whose coupons depend on the occurence of a weather event. The stress is put more on the structuration than on the simple pricing of the bond. Therefore, instead of looking only at the bond issue, we consider it as a part of a more general transaction, involving three agents: a firm, which wants to be hedged against its weather risk, an investor, which buys the bond and a bank, which has an intermediary key role. Then, we derive the optimal characteristics of the whole transaction. But the bond structure which is obtained, corresponds to a minimal structure: indeed, only the bond optimal price function and its optimal reimbursement level (amount which is paid back when an event occurs) can be determined while there is a degree of freedom in the choice of the optimal coupon. Therefore, this indeterminacy may be interpreted as a marketing tool and it could play an important role in the negotiation process between the issuer and the investor.