How do central bank digital currencies (CBDC) impact the balance sheets of banks and central banks? To tackle this question empirically, we built a constraint optimisation model that allows for individual banks to choose how to respond to outflows of deposits, based on cost considerations and subject to the availability of reserves and collateral, within the individual banks and system wide, and for a given level of liquidity risk tolerance. We simulate the impact of a fictitious digital euro introduction in the third quarter of 2021, using data from over 2,000 euro area banks. That impact depends on i) the number of deposits withdrawn and the speed at which this occurs, ii) the liquidity available within the banking system at the time of the digital euro introduction, iii) the liquidity risk preferences of the markets and supervisors, iv) the bank’s business model, and v) the functioning of the interbank market. We find that a €3,000 digital euro holding limit per person, as suggested by Bindseil (2020) and Bindseil and Panetta (2020), would have been successful in containing the impact on bank liquidity risks and funding structures and on the Eurosystem balance sheet, even in extremely pessimistic scenarios.