The overnight rate is generally the interest rate that large banks use to borrow and lend from one another in the overnight market. In some countries (the United States of America, for example), the overnight rate may be the rate targeted by the central bank to influence monetary policy. In most countries, the central bank is also a participant on the overnight lending market, and will lend or borrow money to some group of banks.
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There may be a published overnight rate that represents an average of the rates at which banks lend to each other; certain types of overnight operations may be limited to qualified banks. The precise name of the overnight rate will vary from country to country.