• The total spillover intensity among Chinese carbon bond market, carbon stock market and energy stock market is transitional. • The role of carbon stock market and carbon bond market as net transmitter and receiver of shocks, respectively, are persistent. • We find strong information transmit intensity from carbon stock market to energy stock market and strong information transmit intensity from energy stock market to carbon bond market. In this paper, we employ the time domain dynamic connectedness method of Antonakakis et al. (2020) and the frequency domain dynamic connectedness method of Barunik and Ellington (2020) to explore the complex linkages among Chinese carbon bond market, carbon stock market and energy stock market. We find firstly that the spillover effects among Chinese carbon bond market, carbon stock market and energy stock market are dynamic and mainly transitional. Secondly, carbon stock market and carbon bond market (especially the carbon neutral bond market) play the role of the major net transmitter and receiver of shocks, respectively. And, their roles as net transmitter and receiver of shocks are persistent. Finally, the risks of companies that have achieved effective results in the field of carbon neutrality may bring greater pressure to the energy stock market, but the carbon bond market can alleviate this pressure to a certain extent. Meanwhile, the impact of carbon stock market on energy stock market and the ability of carbon bond market (especially the carbon neutral bond market) to mitigate the risks of the energy stock market is persistent. [ABSTRACT FROM AUTHOR]