A Dynamic Programming Approach for Pricing Weather Derivatives under Issuer Default Risk

Weather derivatives are contingent claims with payoff based on a pre-specified weather index. Firms exposed to weather risk can transfer it to financial markets via weather derivatives. We develop a utility-based model for pricing baskets of weather derivatives under default risk on the issuer side in over-the-counter markets. In our model, agents maximise the expected utility of their terminal wealth, while they dynamically rebalance their weather portfolios over a finite investment horizon. Using dynamic programming approach, we obtain semi-closed forms for the equilibrium prices of weather derivatives and for the optimal strategies of the agents. We give an example on how to price rainfall derivatives on selected stations in China in the universe of a financial investor and a weather exposed crop insurer.