Pricing weather contracts with persistent temperature memory driven by a Fractional Ornstein-Uhlenbeck process

Monday, 23 June 2025

10:30 AM – 12:00 PM

Venue: Gaia Lecture Theatre 5 (#ABS-02-LT5) 

Chairperson: Asst Prof Jinggong Zhang

Abstract

Despite the high persistence observed in temperature series, most prevailing statistical temperature models and weather contract valuation methodologies do not adequately account for long-range dependency, potentially leading to suboptimal temperature forecasts and mispricing of weather-related contracts. In response, we propose the generalized fractional Ornstein-Uhlenbeck (gfOU) process, which captures the trends, seasonality, mean reversion, and long-range dependence inherent in temperature data. We further derive a simplified covariance formula for the stationary fractional Ornstein-Uhlenbeck process and evaluate the consequences of model misspecification when memory effects are erroneously omitted. For the valuation of temperature-linked contracts, we derive closed-form expressions for both the payoff frequency and the expected payoff based on the gfOU temperature process. We demonstrate that our model yields more accurate payoff predictions and enhances insurer profitability within a Bertrand competitive game. Our empirical analysis further validates the presence of temperature persistence across the United States and reveals significant regional variations over recent decades. Additionally, we present evidence that the restricted gfOU model outperforms its benchmark gOU counterpart and the Burn approach in forecasting the payoffs of temperature-linked contracts.

About the Speaker

Jayen is a Nanyang Business School (NBS) International PhD Scholar currently pursuing his doctorate at Cornell University, with an expected graduation in May 2027. He holds a bachelor’s degree in Actuarial Science and a master’s in Financial Engineering from NBS, where he was recognized with several top academic honors, including the Top MFE Student Award, the Singapore College of Insurance Gold Medal, and the IFoA Sir Edward Johnston Award. His research focuses on long-range dependency modeling and weather derivatives.