We propose a model of the interbank money market with an explicit role for central bank intervention, and study how profit-maximizing behavior on the part of banks (facing periodic reserve requirements and daily shocks to liquidity) interacts with high-frequency interest rate targeting. The model delivers a number of predictions on the cyclical behavior of the federal funds rate's volatility and on its response to changes in target rates and changes in intervention procedures, such as those implemented by the Fed in 1994. We find theoretical results to be consistent with empirical patterns of interest rate volatility in the U.S. market for federal funds.