This study uses a quantile autoregressive distributed lag model to quantitatively evaluate the effects of economic policy uncertainty (EPU) and geopolitical risk (GPR) on volatility in carbon futures (carbon trading price [CTP]), considering both quantile and time asymmetries. The findings show that long-term effects of GPR on CTP are more significant than the short-term effects, contrary to EPU. Both EPU and GPR have predominantly positive long-term effects on CTP, while EPU negatively affects CTP and geopolitical factors show mixed influences in the short term. The location asymmetry reveals that the long-term impacts are most pronounced at higher quantiles, whereas the short-term effects exhibit subtle variations across different quantiles. The influences intensify during structural shifts owing to heightened events. Moreover, EPU is proven as a dominant contributor influencing the fluctuation of CTP both in the short and long terms. The findings provide targeted recommendations for policymakers to stabilize CTP and contribute towards achieving sustainable development.