Inflation has tended to be moderate during stock market booms in many countries. To explain the pattern and study optimal monetary policy in such a situation, this paper develops a dynamic model with rational bubbles and nominal rigidities. The model features a financial cost channel through which the shadow cost of borrowing affects marginal costs. A bubble‐led boom mitigates firms' borrowing constraints and keeps inflation from rising by decreasing the shadow cost. In this situation, Ramsey‐optimal monetary policy calls for tightening to curb the boom. Strict inflation targeting is counterproductive in the short run as it exacerbates the boom. For obtaining these results, the financial cost channel and nominal wage rigidity are essential.