Optimal hedging using both regular and weather derivatives

This paper analyses how to achieve optimal hedging of a cash flow to be received at a future date T, when facing price risk, cost and quantity uncertainty. We explore and compare the case where the only instrument available to hedge is a regular forward contract (to hedge the price uncertainty), the case where we only have access to a linear-type weather derivative to hedge quantity, and the case where both types of contracts are available. A closed form solution for both the optimal hedging strategies and the quality of the hedging under each scenario are identified. We show how to obtain the optimal hedging strategies through linear regressions. Then, by using simulations, we explore how the results critically depend on some key factors such as the volatility of some stochastic variables considered and the degree of correlation among some of the variables considered.