We incorporate monetary policy into a model of stochastic debt sustainability analysis and evaluate the impact of unconventional policies on sovereign debt dynamics. The model optimizes debt nancing to trade o nancing cost with renancing risk. We show that the ECB pandemic emergency-purchase programme (PEPP) substantially improves debt sustainability for euro area sovereigns with a high debt stock. Without PEPP, debt would be on an increasing (unsustainable) trajectory with high probability, while, with asset pur- chases, it is sustainable and the debt ratio is expected to return to pre-pandemic levels by about 2030. The improvement in debt dynamics extends beyond the PEPP and is larger for more gradual unwinding of the Central Bank balance sheet. Optimal nancing under PEPP induces an extension of maturities reducing the risk without increasing costs. The analysis also shows that in ation surprises have relatively little impact on debt dynamics, with the direction and magnitude of the eect depending on the monetary policy response.