A critical view on temperature modelling for application in weather derivatives markets

a r t i c l e i n f o JEL classification: C18 C51 Keywords: Temperature Time series model Weather derivatives Seasonality GARCH In this paper we present a stochastic model for daily average temperature. The model contains seasonality, a low-order autoregressive component and a variance describing the heteroskedastic residuals. The model is estimated on daily average temperature records from Stockholm (Sweden). By comparing the proposed model with the popular model of Campbell and Diebold (2005), we point out some important issues to be addressed when modelling the temperature for application in weather derivatives market. In recent years there has been a growing interest in modelling the dynamics of surface air temperature with application in pricing weather derivatives. We follow up this stream of research with a critical discussion on model building and estimation, contrasting two stochastic models proposed by Campbell and Diebold (2005) and Benth and Šaltytė-Benth (2007). Both models are based on a seasonal autoregressive (AR) process, but with significant differences in structure which influences their applicability in relation to temperature derivatives. The two models are widely used in the field, and are similar to or nest a number of related models, see, for example, Dornier and Querel (2000), Alaton et al. (2002), Cao and Wei (2004) to mention a few. The performance (in terms of forecasting weather indices) of various models for temperature dynamics, including the two considered here, was compared by At the Chicago Mercentile Exchange (CME) there is an organized trade in weather futures and options. In particular, the CME offers trade in futures contracts written on temperature indices measured at various locations world wide, providing financial instruments to hedge weather risk exposure. The locations are major cities in the US, Canada, Europe and Asia. The temperature indices measure the daily cumulative average temperature (CAT), the cumulative heating-degree days (HDD) or the cumulative cooling-degree days (CDD). The reference temperature is taken as the average of the daily minimum and maximum temperature, which we further refer to as temperature. More specifically, if we denote the temperature on day t by Z(t), then the CAT index over a measurement period [T 1 , T 2 ] is defined as CAT T 1 ; T 2 ð Þ¼ X T 2 t¼T 1 Z t ð Þ; ð1Þ where the measurement period is typically a given month or season. At CME, CAT futures are traded on European …