Abstract

This paper introduces a new temperature index, which can suitably represent the underlying of a weather derivative. Such an index is defined as the weighted mean of daily average temperatures measured in different locations. It may be used to hedge volumetric risk, that is the effect of unexpected fluctuations in the demand/supply for some specific commodities—of agricultural or energy type, for example—due to unfavorable temperature conditions. We aim at exploring the long term memory property of the volatility of such an index, in order to assess whether there exist some long-run paths and regularities in its riskiness. The theoretical part of the paper proceeds in a stepwise form: first, the daily average temperatures are modeled through autoregressive dynamics with seasonality in mean and volatility; second, the assessment of the distributional hypotheses on the parameters of the model is carried out for analyzing the long term memory property of the volatility of the index. The theoretical results suggest that the single terms of the index drive the long memory of the overall aggregation; moreover, interestingly, the proper selection of the parameters of the model might lead both to cases of persistence and antipersistence. The applied part of the paper provides some insights on the behaviour of the volatility of the proposed index, which is built starting from single daily average temperature time series.

Highlights

  • Weather derivatives represent a particular kind of exotic financial contract introduced to manage the volumetric risk caused by unfavorable weather conditions

  • We focus on a theoretical approach for assessing the long term memory property of a temperature index

  • Via a time series approach, we focus on the Daily Average Temperature (DAT) dynamics of four cities located in the Eastern area of US: Baltimore, Boston, Cincinnati and Philadelphia

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Summary

Introduction

Weather derivatives represent a particular kind of exotic financial contract introduced to manage the volumetric risk caused by unfavorable weather conditions. The informative content of temperature long term memory in terms of financial modelling is clear It is worth mentioning Brody et al (2002) and Benth (2003) who introduce a Ornstein-Uhlenbeck stochastic process driven by a Fractional Brownian Motion for the daily-mean temperature evolution, in the context of weather derivatives. The temperature index proposed here is a weighted average of DATs. we analyze the long term memory of its volatility to an agent-based model. According to the above mentioned contributions, we discuss the distributional hypotheses of the parameters of a temperature index to verify the presence of long term memory in its volatility Since such an index is a weighted aggregation of univariate DATs, we apply a very important result due to Granger (1980).

Daily Average Temperature: a brief review of literature
The model
The assessment of long-term memory
Analysis of the results
An analysis based on observed data
Conclusions
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