The Bank for International Settlements released a working paper analysing how banks’ private arrangements for contingent funding interact with central bank liquidity support during stress. The paper argues that while private contingent capital can eliminate banks’ incentives to overinvest to issue cheap money-like deposits, anticipated central bank interventions can crowd out these private markets and reintroduce overinvestment and fragility if public support is not priced to reflect its incentive effects. Using a fire-sale externality framework based on Stein (2012), the authors show that frictionless private state-contingent funding restores socially efficient outcomes but does not remove fire sales, creating incentives for central banks to intervene ex post. A “bailout” lender of last resort or lending priced at (or below) break-even can induce banks to take on more illiquidity risk and increase investment, while reducing or eliminating demand for private contingent capital. Pre-committed central bank liquidity facilities can reduce these distortions but only if priced above actuarially fair levels in line with a “Bagehot” penalty that reflects private fire-sale costs, which the paper argues may be politically difficult to sustain; central bank “myopia” further worsens outcomes. An extension incorporating leveraged speculative activities with margin calls shows that cheap public liquidity can amplify crisis liquidity demand and welfare losses. The paper was presented at the 24th BIS Annual Conference in Basel on 27 June 2025 and released as part of the BIS Working Papers series.