Incorporating Spatial Dependence and Climate Change Trends for Measuring Long-Term Temperature Derivative Risk

By Robert J. Erhardt

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In this paper we explore a method to model the financial risks of holding portfolios of long-term temperature derivatives for any subset of the 30 North American cities whose derivatives are actively traded on the Chicago Mercantile Exchange (CME). Long-term derivatives are those whose period of accrual for degree days is substantially longer than the temporal auto correlation of daily temperature data, and therefore accruals can be modeled with a multivariate normal distribution. One commonly traded temperature derivative on the CME has a 6-month index period, which satisfies this long-term condition. The method presented incorporates spatial dependence among the cities, and allows for possible trends in degree days due to climate change. Though limited to long-term contracts, the method is mathematically and computationally quite simple and applicable to some of the most commonly traded temperature derivatives. Possible implications for the insurance industry are discussed.

Keywords: Chicago Mercantile Exchange, cooling degree day, heating degree day, weather derivative


Erhardt, Robert J., "Incorporating Spatial Dependence and Climate Change Trends for Measuring Long-Term Temperature Derivative Risk," Variance 9:2, 2015, pp. 213-226.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.