Stochastic Temperature Modeling Using the Ornstein-Uhlenbeck Process for Fractional Dimensional Weather Derivative Pricing in Climate Risk Management

Temperature variability and weather-related fluctuations significantly affect the energy, agricultural, and industrial sectors that are highly sensitive to meteorological changes. These conditions may lead to financial losses caused by demand fluctuations and operational disruptions. This study aims to develop a fractional weather-derivative pricing model based on temperature dynamics by integrating the Ornstein–Uhlenbeck (OU) process, the classical Black–Scholes model (BSM), and the fractional Black–Scholes model (fBSM). Daily temperature data from 2016 to 2025 obtained from the Bandung Geophysical Station, West Java, Indonesia, were used as the basis of analysis. Temperature dynamics were modeled using an OU process, and parameter estimation was conducted using Ordinary Least Squares (OLS). The strike price was determined using Historical Burn Analysis (HBA), whereas weather-derivative pricing was performed using call and put option approaches under both the BSM and fBSM frameworks, incorporating the Hurst parameter to capture long-term memory effects. The results indicate that the fractional Black–Scholes model analytical solution is obtained using the Daftardar–Gejji Aboodh method. Furthermore, the OU process successfully captured daily temperature dynamics, yielding a Mean Absolute Percentage Error (MAPE) of 4.344% and a Root Mean Square Error (RMSE) of 1.396 C, indicating high predictive accuracy across both relative and absolute error measures. In addition, the fBSM consistently generated higher option values than the classical BSM, particularly under higher observed temperatures during the study period and at higher strike prices. These findings demonstrate that long-term memory significantly influences effective volatility and option valuation. This study is expected to contribute to the development of weather derivative models that more realistically represent temperature dynamics and to serve as a reference for weather derivative pricing, hedging, and decision-making, as well as for more measurable, systematic, and sustainable climate-related financial analysis using derivative pricing frameworks.