Speculation and policy credibility are increasingly debated as drivers of EU ETS price dynamics, yet they are typically analysed separately. This is problematic because credibility and speculation interact through firms' banking and compliance decisions: doubts about future policy weaken banking and depress prices, while speculative trading can amplify price movements and feed back into perceived credibility by shaping abatement incentives and realised emissions. We develop a dynamic behavioural model in which credibility evolves endogenously with ETS performance. Compliance firms choose abatement and bank more when credibility is higher, while heterogeneous financial traders take positions in permit futures using fundamentalist and trend-following expectations, alongside noise trading. We show that a policy-anchored equilibrium is locally stable when credibility-sensitive banking provides a strong anchor, but self-fulfilling speculative equilibria emerge when trend-following dominates. Calibrated simulations for 2023-2050 indicate that fundamentals-anchored trading can reinforce credibility, support higher prices and abatement, and reduce cumulative emissions, while an MSR reform scaling thresholds with the declining cap improves late-transition control over the net-zero date.