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This article studies the stabilization effect of monetary policy reacting to asset price, accounting for the expectations formation effect of policy regime shift, in a DSGE model calibrated to the US economy. In contrast to the linear policy rule that generates negligible stabilization effect from responding to asset prices, the regime switching policy rule can significantly stabilize inflation-output volatilities. We then identify the range of parameter values that can generate stabilization effect for inflation and find that reacting to asset prices too aggressively can be inflation destabilizing. Given certain combinations of parameter values, the trade-off between the expected volatility of inflation and that of output, as demonstrated by the Taylor curve, substantially diminishes, thus considering non-linear policy rule expands the set of monetary policy choices available for monetary authority. Finally, there exists an optimal responsiveness to asset prices.