Joint Optimal Ordering and Weather Hedging Decisions: A Newsvendor Model

This paper considers the problem of hedging inventory risk for a seasonal product whose demand is sensitive to weather conditions, such as the average seasonal temperature. The newsvendor not only decides the order quantity, but also adopts a weather hedging strategy. A typical hedging strategy is to use a weather derivative (such as an option) that is constructed on a weather index before the season begins, which will compensate the buyer of the option if the actual seasonal weather index is above (or below) a given strike level. We explore the joint decision problem in both the conditional value-at-risk framework and the general utility-maximization framework. Under the former, the newsvendor attempts to maximize an objective that trades off the expected profit with the conditional value-at-risk (CVaR), whereas; under the latter, the newsvendor tries to maximize his expected utility. The use of CVaR as a risk measure holds certain advantages over that of utility, one of which is that the only subjective parameter for CVaR is the confidence level. This is important for applications of the model. We establish structural properties for the optimal decisions under both frameworks and analyze the impact of weather hedging on his optimal order quantity. Among the main contributions of the paper are recognizing the need for joint determination of order quantity and weather hedging and analyzing how the introduction of weather derivatives (options) affects the optimal ordering quantity. In addition, the paper also shows that the different derivatives have different impacts on the newsvendor, and it is thus important for him to choose the right hedging derivative(s).