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Carbon option pricing based on uncertain fractional differential equation: A binomial tree approach

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  • Liu, Hanjie
  • Zhu, Yuanguo

Abstract

In this paper, we use a Caputo–Hadamard uncertain fractional differential equation (UFDE) to describe the change of carbon emission rights price. Based on a binomial tree approach, a portfolio is constructed by buying options and shorting the underlying assets in a certain proportion. The pricing formulas for carbon finance European option are presented, and the algorithms are designed to formulate the price of carbon finance American option without explicit pricing formulas. Besides, a moment estimation method is used to obtain the parameter values in Caputo–Hadamard UFDE, and a method is provided to simulate the observation data of solution of Caputo–Hadamard UFDE. Finally, the specific Caputo–Hadamard UFDE with mean-reverting process is applied to simulating the change of carbon emission rights price in Chinese carbon market, and the feasibility of the proposed carbon option pricing method is illustrated by some numerical examples.

Suggested Citation

  • Liu, Hanjie & Zhu, Yuanguo, 2024. "Carbon option pricing based on uncertain fractional differential equation: A binomial tree approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 13-28.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:13-28
    DOI: 10.1016/j.matcom.2024.05.007
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    Cited by:

    1. Lifen Jia & Linya Zhang & Wei Chen, 2024. "China’s carbon emission allowance prices forecasting and option designing in uncertain environment," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 539-560, December.

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