One explanation for large stock market fluctuations is its tendency to herd behavior. We put forward an agent-based model where instabilities are the result of liquidity imbalances amplified by local interactions through imitation, and calibrate the model to match some key statistics of actual daily returns.We show that an “aggregate market-maker” type of liquidity injection is not successful in stabilizing prices due to the complex nature of the stock market. To offset liquidity shortages, we propose the use of locally triggered contrarian rules, and show that these mechanisms are effective in preventing extreme returns in our artificial stock market.