The paper models the links between financial fragility, asset markets and monetary policy. It is shown that central bank's concern about the cost of financial disruption generates an asymmetric response, thus contributing to the creation of an asset price bubble. In an economy with a highly leveraged financial structure, the central bank has an incentive to prevent a 'run' on financial intermediation by injecting liquidity when asset values fall significantly. The inflationary side effect of this policy reduces the real value of nominal debt and so gives rise to a 'put option' for investors, driving up asset prices above their fundamental value. The paper shows that the size of such a bubble is likely to be rather small. The bubble is only equal to the expected value of capital gains on outstanding debt, which are fairly limited in a crisis. Since, in contrast, the gains from preventing the disruption of financial intermediation can be quite large, it is rational for a central bank to inject liquidity in a crisis.