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

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 autocorrelation 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.