With the global acknowledgment of the Kyoto Protocol came the carbon derivatives such as carbon futures, options, and swap contracts. The innovative carbon derivatives are complex in design and contain risks that are difficult to predict and avoid. The global Carbon Market should have higher requirements in the supervision laws and regulations. To this end, the financial system theories and the financial characteristics of carbon derivatives are expounded. The three-dimensional structural modeling technique of systems engineering is introduced to construct the Carbon Market framework. The proposed framework factors for the organization, product, and policy dimensions of the Carbon Market are also described. Additionally, this model explains the market organization, the instruments and media connecting market supply and demand, and government regulation measures. In particular, the supervision and management aspects of the policy dimension are introduced in detail. The Carbon Market and relevant law systems in the United States, the European Union, and India are mainly studied and compared. Based on the comparison results, the necessity of market supervision is explained. Finally, the Big Vector Autoregression model is used to study the relationship between the Carbon Market, energy market, and financial market. After the introduction of the National Carbon Market, the correlation between the energy market and the financial market has become relatively complex but also presents a certain degree of asymmetry. According to the above results, the paper proposes to use the “regulatory sandbox” mechanism to improve the regulation of the subject and object of the carbon financial and legal relationship and try to carry out regulatory innovation for the risks of the entire carbon market.