With the initiation of China's "dual-carbon" strategy, carbon risk has emerged as a pivotal constraint on the nation's high-quality economic development. This paper employs the Pressure-State-Response (PSR) conceptual framework to formulate an evaluation index system encompassing policy risk, market risk, and technological risk. The assessment utilizes the projection pursuit (PP) model to gauge carbon risk in six Chinese provinces and cities—Beijing, Tianjin, Shanghai, Chongqing, Hubei, and Guangdong—from 2016 to 2021. Additionally, the paper employs the geographic detector (GD) to scrutinize the driving mechanisms of carbon risk among these provinces. Key findings include: (1) Overall carbon risk levels: From 2016 to 2021, Tianjin exhibited the highest carbon risk, while Guangdong had the lowest. Despite a downward trend in carbon risk levels across provinces and cities, by 2021, the majority of regions still maintained relatively high levels of carbon risk. (2) Single risk factor analysis: Shanghai and Guangdong demonstrated lower policy risks, Chongqing exhibited lower market risks, and Guangdong showcased lower technological risks. Policy risks followed a hierarchical distribution among provinces and cities. Excluding Guangdong, technological risks consistently surpassed policy risks and market risks, underscoring the severity and challenges in the technological domain. (3) Driving factors of carbon risk: The intensity of investment in environmental governance and the rationality of industrial institutions emerged as pivotal factors influencing carbon risk. The interaction of these factors bolstered the explanatory power of carbon risk outcomes, highlighting that a comprehensive response is more efficacious in mitigating carbon risk. The findings constitute crucial references for the government's formulation of effective strategies for the prevention and control of carbon risk.

PSR framework; carbon risk; projection pursuit; geodetector