Central banks have won in credibility as from the mid-eighties by keeping inflation under control. However, confidence in low inflation might have encouraged agents to excessive risk-taking, leading asset prices to rise. Moreover, the belief in a Federal Reserve guarantee against a sharp market decline spread across US markets as from the nineties. This belief, commonly referred to as the Greenspan put, raised again the question about the role of asset prices in monetary policy decisions. The problem is addressed by modeling the reaction of the Fed to stockmarket deviations from fundamentals over the period stretching from August 1987 to October 2008, which corresponds to the periods where Greenspan until January 2006 and Bernanke from thereon were chairmen. A Taylor rule describing the Fed's nominal feedback rule to inflation and economic activity on a monthly basis is extended to take account of asset prices. The indicators considered are deflation and volatility in stock prices. Furthermore, a Markov switching process allows to capture contemporaneous as well as forward-looking monetary policy responses to asset prices over the period. We find out that taking asset price deflation improves the Taylor rule fit by some 8%. In periods when the Fed was actively pursuing an expansive or restrictive monetary policy, its reaction to volatility or deflation of financial markets was significant. We also see that the reaction of the Fed to asset prices was greater during financial crises, especially when modeling a forward-looking decision process. Agents' confidence in a stronger response of the US central bank to significant market declines urging to an easing of monetary conditions in their favour was therefore not unfounded.