Pricing and valuation of carbon swap in uncertain finance market

It has become a consensus in the international community to actively address global climate change issues and strive to achieve carbon reduction. For this purpose, carbon finance market plays a significant role in reducing carbon emissions by providing financial mechanisms to support and incentivize emission reduction projects. As a type of carbon finance derivative, carbon swap is an agreement between two parties whereby a floating price is exchange for a fixed price for carbon emission right over a specified period. How to price carbon swap before signing, i.e., determine the fixed price in the swap contract, and valuate carbon swap during the life of the swap contract are key issues. Noting the fact that the underlying asset of carbon swap is carbon price, the primary task is to model carbon price reasonably. Due to the inherent challenges and uncertainties associated with pricing carbon, frequency stability is often not guaranteed, resulting in the failure of probability based methods. Thus, this paper characterizes the carbon price using uncertain differential equation under the framework of uncertainty theory, and derives swap pricing and valuation formulas. Estimations for unknown parameters in the proposed model are given. Finally, with carbon spot price in European Energy Exchange, real data analyses are documented to illustrate our proposed methods in details.