Investigates pricing models for carbon swaptions, highlighting their applicability in uncertain markets.
Within the framework of uncertainty theory, this paper employs a Caputo-Hadamard uncertain fractional differential equation to model the dynamics of carbon emission allowance prices and investigates the pricing of carbon swaptions. Based on the constructed model, analytical expressions for the prices of carbon swaptions are derived. Actual trading data from the Shanghai Environment and Energy Exchange's national carbon market for December 2024 to December 2025 are selected to estimate the model's unknown parameters using the method of moments, and the model's validity is verified through uncertainty hypothesis testing. The results indicate that the Caputo-Hadamard uncertain fractional differential equation effectively captures the dynamic characteristics of long-term carbon emission allowance prices. The proposed pricing methods demonstrate good applicability and can provide theoretical foundations and quantitative tools for risk management and contract design for carbon market participants under conditions of information asymmetry and market incompleteness.
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Fang et al. (2026) studied this question.
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