Although the case for a swift climate transition is clear, its macro-financial viability remains uncertain. To shed light on the macroeconomic and financial response to deep mitigation trajectories controlled by carbon pricing, we integrate a process-based integrated assessment model into a macroeconomic agent-based model. The hybrid framework allows translating energy systems transformations into macro-financial outcomes at business cycle frequency and volatility. The results reveal that rapid transitions induced by fast-growing carbon prices significantly impact unemployment, inflation, and income distribution. Stabilization policies reduce these economic fluctuations, though not completely so in 1.5°C compatible scenarios. Our paper emphasizes the need for coordinating climate and macroeconomic policy during decarbonization. Additionally, it showcases how model integration can lead to a better understanding of the economic implications of low-carbon futures.