Carbon option pricing and carbon management under uncertain finance theory

Against the backdrop of increasingly severe global climate change issues, more and more countries and regions are adopting carbon emission trading, which is an effective market mechanism. As an important component of the carbon market, American carbon options provide more flexible trading tools to help companies avoid price risks. Therefore, the pricing research of American carbon options is of great significance for promoting the healthy development of the carbon market. Nonetheless, existing pricing methods are all based on probability theory, which need to satisfy the premise that the distribution function is close to the true frequency sufficiently. However, usually such premise is ill-suited in carbon market. To alleviate the predicament of the need for satisfying probability theory's premise, this work investigates American carbon option pricing under the framework of uncertainty theory, which is another axiomatic mathematical system. For this purpose, uncertain differential equation is adopted to model the price of carbon future, and pricing formulae for American call and put carbon options are derived based on this model. Real data analyses illustrate the proposed method in details. Furthermore, it provides a detailed schema of applying the American carbon option for carbon asset management, which can optimize risk control for carbon consuming enterprises.