Stochastic Models for Pricing Weather Derivatives using Constant Risk Premium

Pricing weather derivatives is becoming increasingly useful, especially in developing economies. We describe a statistical model based approach for pricing weather derivatives by modeling and forecasting daily average temperatures data which exhibits long-range dependence. We pre-process the temperature data by filtering for seasonality and volatility and fit autoregressive fractionally integrated moving average (ARFIMA) models, employing the preconditioned conjugate gradient (PCG) algorithm for fast computation of the likelihood function. We illustrate our approach using daily temperatures data from 1970 to 2008 for cities traded on the Chicago Mercantile Exchange (CME), which we employ for pricing degree days futures contracts. We compare the statistical approach with traditional burn analysis using a simple additive risk loading principle for pricing, where the risk premium is estimated by the method of least squares using data on observed prices and the corresponding estimate of prices from the best model we fit to the temperatures data.