Utility-based pricing of weather derivatives

Since the underlying of the weather derivatives is not a traded asset, these contracts cannot be evaluated by the traditional financial theory. Cao and Wei [2004. Weather derivatives valuation and market price of weather risk. The Journal of Futures Markets 24, no. 11: 1065-89] price them by using the consumption-based asset pricing model of Lucas [1978. Asset prices in an exchange economy. Econometrica 46, no. 6: 1429-45] and by assuming different values for the constant relative risk aversion coefficient. Instead of taking this coefficient as given, we suggest in this article to estimate it by using the consumption data and the quotations of one of the most transacted weather contracts which is the New York weather futures on the Chicago Mercantile Exchange. We apply the well-known generalized method of moments introduced by Hansen [1982. Large sample properties of generalized method of moments estimators. Econometrica 50, no. 4: 1029-54] to estimate it as well as the simulated method of moments (SMM) attributed to Lee and Ingram [1991. Simulation estimation of time-series models. Journal of Econometrics 47, no. 2-3: 197-205] and Duffie and Singleton [1993. Simulated moments estimation of Markov models of asset prices. Econometrica 61, no. 4: 929-52]. This last method is studied since it is presumed to give satisfactory results in the case of the weather derivatives for which the prices are simulated. We find that the estimated coefficient from the SMM approach must have improbably high values in order to have the calculated weather futures prices matching the observations.