Pricing Temperature-Index Insurance under Long Memory and Stochastic Time Change
This study addresses the challenge of neglecting long memory and stochastic time-varying characteristics in temperature index insurance pricing by constructing an actuarial framework based on fractional Brownian motion and the CIR process. By deriving conditional Gaussian representations and exact kernel functions, combined with Monte Carlo simulation, the proposed approach achieves efficient valuation while avoiding complex path simulations. Empirical results demonstrate that this model significantly enhances the accuracy of climate risk pricing and reveals the substantial impact of long memory and time-varying properties on premiums. Consequently, this work provides innovative methodological support for advancing weather derivative pricing theory, effectively bridging the gap between sophisticated stochastic modeling and practical actuarial applications in managing temperature-related financial risks.