Putting a Price on Temperature*

Abstract

This paper analyzes the weather derivatives traded at the Chicago Mercantile Exchange (CME), with futures and options written on different temperature indices. We propose to model the temperature dynamics as a continuous-time autoregressive process with lag "p" and seasonal variation. The choice ""p"=3" turns out to be sufficient to explain the temperature dynamics observed in Stockholm, Sweden, where we fit the model to more than 40 years of daily observations. The main finding is a clear seasonal variation in the regression residuals, where temperature shows high variability in winter, low in autumn and spring, and increasing variability towards the early summer. Our model allows for derivations of explicit prices for several futures and options. Note that the volatility term structure of futures written on the cumulative average temperature has a "modified" Samuelson effect, where the volatility prior to the measurement period increases, except for the last part, where it may decrease. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..

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

“…In Benth et al [4,7], the choice of K = 3 turned out to give a very good As already mentioned, in many locations one finds signs of GARCH effects in the residuals after removing the influence of σ BSB (t) (that is, in the data ε(t)/σ BSB (t)). Such effects are minor, but to explain them in the proposed model it is natural to assume that σ(t) = σ BSB (t)σ GARCH (t) with…”

“…The stability analysis of AR(1) process was performed in Benth et al [7] for Stockholm temperatures. There were no significant differences observed among the regression parameters estimated for different years or seasons.…”

“…Higher-order AR models have been proposed and analysed by Benth et al [28,7] for data in Sweden and Lithuania. Recently, such models have been extended to Berlin data and several Asian cities by Härdle and Lopez Cabrera [20] and Benth et al [9].…”

“…A model should incorporate such properties as possible trend due to global warming and/or urbanisation, seasonal component describing periodic temperature variations related to cold and warm seasons, AR properties for temperature changes, and seasonal variations in residuals. In this study, we follow up the analysis from papers Benth andŠaltytė Benth [5], Benth et al [7],Šaltytė Benth et al [28], and contrast it to the approach of Campbell and Diebold [14].…”

“…First, we critically review the process of modelling the temperatures. In this paper we promote a stepwise procedure used in [5,7,28], where one models and estimates each component step-by-step. This turns out to be advantageous in order to build a confident model explaining the various stylized facts of temperature.…”