Pricing weather contracts under persistent memory in temperature

Abstract Although temperature dynamics exhibit pronounced long‐memory behavior, most existing temperature models and weather derivative valuation frameworks neglect such persistence, leading to biased forecasts and systematic mispricing. We propose the generalized fractional Ornstein‐Uhlenbeck (gfOU) process that parsimoniously incorporates time‐varying trends and seasonality while capturing both short‐ and long‐range dependence. Under the stationary fOU process, we derive a tractable closed‐form autocovariance function, quantify the implications of misspecification, and obtain weather contract prices under the risk‐neutral valuation framework. Incorporating long memory yields economically material improvements in forecast accuracy, insurers' profitability, and reserve adequacy. Empirical results reveal substantial spatial and temporal heterogeneity in temperature persistence across the continental United States. The predictive gains of the gfOU model primarily reflect its ability to exploit long‐memory dynamics embedded in historical temperature realizations.