Problem
Research questions and friction points this paper is trying to address.
Temperature-index insurance pricing
Long memory
Stochastic time change
Fractional Brownian motion
Capped cumulative index
Pricing Temperature-Index Insurance under Long Memory and Stochastic Time Change
🤖 AI Summary
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.
📝 Abstract
This paper develops a unit-consistent actuarial framework for pricing capped cumulative temperature-index insurance under long-range dependence and stochastic variability. Daily temperature anomalies are modeled as increments of fractional Brownian motion evaluated at an operational time generated by the integral of a stationary normalized Cox--Ingersoll--Ross process. We show that the stochastic time change preserves stationarity and the long-memory covariance decay of the increments while introducing additional variability through the random operational clock. The cumulative temperature index admits a conditionally Gaussian representation, which leads to an exact conditional exponential kernel for capped stop-loss contracts and ensures existence of the entropic premium for every positive risk-aversion parameter. Consequently, valuation reduces to an outer Monte Carlo expectation over the accumulated CIR time, avoiding fractional Brownian path simulation and covariance-matrix construction. We further establish monotonicity properties of the premium with respect to risk aversion and conditional volatility. An empirical illustration based on Chicago temperature data shows that both long memory and stochastic time change can materially affect insurance premiums relative to conventional Brownian and fractional Brownian benchmarks, with the Hurst parameter playing an important role in valuation uncertainty. The proposed framework therefore provides a tractable approach for incorporating persistent dependence, stochastic variability, and bounded insurance losses into climate-index pricing.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Stochastic Time Change
Fractional Brownian Motion
Temperature-Index Insurance
Entropic Premium
Long Memory
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