Carbon allowance prices (CAP) directly reflect the overall movement of the carbon market, which is the core of the carbon market operation and an important perspective for studying the carbon market. Based on the threshold model and regime switching model, through studying the performance of CAP in China’s carbon market, the paper has the following conclusions. First, CAP show significant non-linear structure and three operating intervals of high, medium, and low, with most of the time being active in the medium and low intervals. Second, there is a stabilization mechanism in the current operation of CAP, which can adequately regulate the trend of CAP fluctuations and eventually converge back to the normal state. Finally, it is found that moderate increases are the main form of CAP volatility in China’s carbon market, but other possible states and the risk of abnormal CAP volatility due to state transformation still exist. Furthermore, for investors, China’s carbon market may be an ideal place to make long-term investments and hedge risks in the future. This paper provides theoretical support for investors and regulators in the carbon market to make scientific decisions based on the carbon market.