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Emission trading scheme (ETS), the most popular market-based instrument, is widely used to solve carbon emission problems in the world. With the development of carbon market, carbon asset has been a popular financial product to invest and the risk management becomes important for government, regulated enterprises and other investors. As carbon prices have tail characteristics, this paper explores the extremal risks between carbon markets in US, Europe and China using tail dependence correlation coefficients. The empirical analysis demonstrates the tail dependence structure between carbon markets in US. and Europe is the same sign, which indicates that it is unwise to hold these two carbon assets as a portfolio. Moreover, the co-movements between European Union Emission Trade Scheme (EU ETS) and China's carbon markets are partly significant, and the operation mechanisms in China should be improved. In addition, the tail dependence test among the carbon pilots in China shows diversity. Hubei carbon trading pilot, located in central China, has extremal dependence with all other selected pilots for its regulatory program operation. The findings give insight to the carbon market regulars to improve the operation mechanism and are also useful for the investors to manage their portfolios, policymakers to make practically applicable regulations, and relevant organizations to develop procedures. [ABSTRACT FROM AUTHOR]