Equilibrium Valuation of Weather Derivatives¤

This paper proposes and implements an equilibrium valuation framework for weather derivatives. We generalize the Lucas model of 1978 to include the weather as a fundamental variable in the economy. The model is specialized to temperature derivatives. Temperature behavior for the period of 1979-1989 is closely studied for ̄ve major cities in the U.S., and a model is proposed for the daily temperature variable which incorporates all the key properties of temperature behavior including seasonal cycles and uneven variations throughout the year. The temperature variable a®ects the aggregate output both contemporaneously and in a lagged fashion. The temperature system is estimated using the 20-year data and numerical analyses are performed for forward and option contracts on heating degree days (HDD's) and cooling degree days (CDD's). The key advantages of our model include the use of weather forecasts as inputs and the ability to handle contracts of any maturity, for any season. Numerical analyses show that the market price of risk associated with the temperature variable is insigni ̄cant in most cases, especially when the aggregate dividend process exhibits mean reversion. The market price of risk becomes important when the risk aversion is high or when the aggregate dividend process is close to a random walk. Finally, we show that the so-called historical simulation method can lead to signi ̄cant pricing errors due to its erroneous implicit assumptions. ¤ The previous version of this paper was titled \Pricing Weather Derivatives: an Equilibrium Approach". We are grateful to the Social Sciences and Humanities Research Council of Canada for ̄nancial support. We, respectively, also acknowledge Queen's Edith Whyte research grant and the University of Toronto Connaught Fund. We thank workshop participants at the Fields Institute, Michigan State University, Ontario Power Generations Company, Queen's University, and York University, and especially Ted Neave, Raymond Ross and Sam Tian for their comments. Equilibrium Valuation of Weather Derivatives