Pricing weather contracts under persistent memory in temperature
针对现有温度模型忽视长期记忆导致定价偏差的问题，提出广义分数阶奥恩斯坦-乌伦贝克过程，在风险中性框架下推导出天气合约定价公式，实证表明考虑长期记忆能显著提升预测精度和保险公司盈利能力。
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.