Seasonality in the statistics of surface air temperature and the pricing of weather derivatives

Abstract

The pricing of weather derivatives motivates the need to build accurate statistical models of daily temperature variability. Current published models are shown to be inaccurate for locations that show strong seasonality in the probability distribution and autocorrelation structure of temperature anomalies. With respect to the first of these problems, we present a new transform that allows seasonally varying non-normal temperature anomaly distributions to be cast into normal distributions. With respect to the second, we present a new parametric time-series model that captures both the seasonality and the slow decay of the autocorrelation structure of observed temperature anomalies. This model is valid when the seasonality is slowly varying. We also present a simple non-parametric method that is accurate in all cases, including extreme non-normality and rapidly varying seasonality. Application of these new methods in some realistic weather derivative valuation examples shows that they can have a very large impact on the final price when compared to existing methods.