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

In this paper, we use a Caputo-Hadamard uncertain fractional differential equation (UFDE) to describe the changes 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.