On Modelling and Pricing Weather Derivatives Peter Alaton Fat Tails Financial Analysis AB¤ Boualem Djehiche and David Stillberger Dept. of Mathematics, KTH y Abstract The main objective of this work is to find a pricing model for weather derivatives with payouts depending on temperature. We use historical data to first suggest a stochastic process that describes the evolution of the temperature. Since temperature is a non-tradable quantity, we obtain unique prices of contracts in an incomplete market, using the market price of risk. Numerical examples of prices of some contracts are presented, using an approximation formula as well as Monte Carlo simulations. ¤Kungsgatan 37 2tr, SE-111 56 Stockholm. e-mail:
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[email protected] 1 Introduction The weather has an enormous impact on business activities of many kinds. The list of businesses subject to weather risk is long and includes, for example, en- ergy producers and consumers, supermarket chains, the leisure industry and the agricultural industries. But it is primarily the energy sector that has driven the demand for weather derivatives and has caused the weather risk management industry to now evolve rapidly. The main aim of this paper is to find a pricing model for weather derivatives. These are financial contracts with payouts that depend on the weather in some form. The underlying variables can be for exam- ple temperature, humidity, rain or snowfall. Since the most common underlying variable is temperature, only temperature based derivatives will be considered here. There are a number of factors behind the growth of the weather derivatives market.