First, before the burst of a bubble, monetary policy should respond to asset price movements, whether driven by the fundamentals or not, only to the degree that those movements have implications for future inflation and economic growth.
Monetary policy should not go beyond that or should not step into “extra operations,” by which I mean a policy decision to intentionally deviate from a monetary policy rule, like the Taylor rule. Second, in contrast to the bubble period, central banks should be proactive after the burst of a bubble.