Weather Derivatives in a Renewal Setting with Uncertain Jumps: A Pricing Approach

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DOI: https://doi.org/10.28924/2291-8639-23-2025-262
Published: Oct 29, 2025
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Zulfiqar Ali, Tareq Saeed, Javed Hussain, Weather Derivatives in a Renewal Setting with Uncertain Jumps: A Pricing Approach, Int. J. Anal. Appl., 23 (2025), 262.

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Zulfiqar Ali, Tareq Saeed, Javed Hussain

Abstract

We develop a novel framework for modeling temperature dynamics and pricing weather derivatives within the setting of Uncertainty Theory. The temperature process is described by a mean-reverting uncertain differential equation with jumps, where continuous uncertainty is modeled via a canonical Liu process and abrupt changes are captured using an uncertain renewal process. This structure yields uncertainty distributions for temperature indices such as Heating Degree Days (HDD) and Cooling Degree Days (CDD), enabling derivative pricing without relying on traditional probability measures or risk-neutral assumptions. By replacing stochastic processes with uncertain ones, the model accommodates belief-driven dynamics and subjective economic impacts, making it especially useful in environments with limited historical data or ambiguous risk. The approach offers a robust and flexible alternative for derivative valuation in both theoretical and applied contexts.

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