Pricing the Weather Derivatives in the Presence of Long Memory in Temperatures

Weather derivatives are financial contracts for which the underlying is not a traded asset. Therefore, they cannot be priced by the traditional financial theory based on the hedging portfolio and on the arbitrage-free argument. Some authors suggest to use the actuarial pricing approach to value the weather derivatives. But this method suffers from the fact that it is only based on the modelling of the temperature. The market information is not necessary to value the weather derivatives by this approach. On the contrary, the financial method needs to infer the market price of weather risk since the market is incomplete for the weather derivatives. We suggest in this paper to compute and to compare the prices stemming from the both approaches by using the New York weather futures quotations. Prices are calculated on the basis that the daily average temperature has a long memory since tests reveal its presence in the serie.