Stochastic Models for Pricing Weather Derivatives using Con- stant Risk Premium

Pricing weather derivatives is becoming increasingly useful, especially indeveloping economies. we describe a statistical model based approach for pricingweather derivatives by modeling and forecasting daily average temperature data whichexhibits long-range dependence. we pre-process the temperature data by filtering forseasonality and volatility and fit autoregressive fractionally integrated moving average(arfima) models, employing the preconditioned conjugate gradient (pcg) algorithmfor fast computation of the likelihood function. we illustrate our approach usingdaily temperature data from 1970 to 2008 for cities traded on the chicago mercantileexchange (cme), which we employ for pricing degree days futures contracts. wecompare the statistical approach with traditional burn analysis using a simple additiverisk loading principle for pricing, where the risk premium is estimated by the methodof least squares using data on observed prices and the corresponding estimate of pricesfrom the best model we fit to the temperature data.