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This paper proposes carbon-based nodal pricing, which utilizes carbon-tracing analysis in its structure. The carbon-tracing algorithms enable the independent system operator (ISO) to better manage and establish a fair pricing mechanism, considering the actual contribution of each plant to the network's total daily emissions. The ISO, by utilizing carbon-tracing analysis, can easily compute nodal carbon intensity and branchial carbon flow, which are used in nodal pricing analysis. Furthermore, in this paper, for motivating flexible consumers, especially those who have higher impacts on carbon emissions, a carbon-based incentive framework called the flexible carbon-responsive (FCR) program is established, which helps the consumers control their carbon output and enables the ISO to decrease the network's total carbon emissions. In the proposed structure, the worst-case scenarios, which arise from uncertain parameters, can easily affect the simulation results. As a result, in order to avoid such issues, analyzing risks associated with uncertainty is the next focus of this research, and the downside risk constraints (DRC) approach is used to accomplish so. The DRC technique helps the ISO achieve an appropriate balance between the cost associated with risk and the anticipated cost, with the simultaneous objective of minimizing overall risk. Last, a modified IEEE 24-bus transmission system and the IEEE 20-bus gas network are utilized to evaluate the suggested carbon-based pricing mechanism. The simulation results show that applying the FCR program and carbon-based pricing causes the total operation costs to decrease by 100%, resulting in an increase of only 0.71% under the proposed DRC method. It could be noted that the total operation cost increment in the with-carbon tax case is 0.18% lower compared to the no-carbon tax policy. • Nodal electricity and gas pricing from environmental roles and carbon taxation. • Flexible carbon-responsive program using nodal carbon-driven pricing. • Modeling carbon-based behavior of consumers using carbon elasticity concept. • Stochastic-driven modeling of uncertainties in renewable generation and demands. • Assessing the risk arising from uncertainties for possible adverse conditions. [ABSTRACT FROM AUTHOR]