Weather Forecasting for Weather Derivatives

Abstract

Weather derivatives are a fascinating new type of Arrow-Debreu security, making pre-specified payouts if pre-specified events occur, and the market for such derivatives has grown rapidly. Weather modeling and forecasting are crucial to both the demand and supply sides of the derivatives market. On the demand side, to assess the potential for hedging against surprises and to formulate the appropriate hedging strategies, one needs to determine how much weather noise exists for derivatives to eliminate, and that requires modeling and forecasting. On the supply side, standard approaches to arbitrage-free pricing are irrelevant in derivative contexts, and so the only way to price options reliably is again by modeling and forecasting the underlying variable. Curiously, however, little thought has been given to the crucial question of how best to approach modeling and forecasting in the context of derivative demand and supply. The vast majority of extant forecasting literature has a structural atmospheric science feel, and although such an approach may be best for forecasting six hours ahead, it is not obvious that it is best for the longer horizons relevant for derivatives, such as six days, six weeks, or six months. In particular, good forecasting does not necessarily require a structural model. In this paper, then, we take a seemingly-naive nonstructural time-series approach to modeling and forecasting daily average temperature in ten U.S. cities, and we inquire systematically as to whether it proves useful. The answer is, perhaps surprisingly, yes. Time series modeling reveals a wealth of information about both conditional mean dynamics and the conditional variance dynamics of average daily temperature, some of which seems not to have been noticed previously, and it provides similarly sharp insights into both the distributions of and the distributions of surprises, and the key differences between them. The success of time-series modeling in capturing conditional mean dynamics translates into successful point forecasting, a fact which, together with the success of time-series modeling in identifying and characterizing the distributions of surprises, translates as well into successful density forecasting.