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Libor, a daily rate in a range of currencies, is based on submissions from banks of interest rates they believe they would be charged by others for borrowing money. Banks have been fined billions of dollars for trying to manipulate the benchmark, forcing a rethink of its future.
The benchmark is used to price financial contracts worth $350 trillion, ranging from home loans to credit cards, and Bank of England Governor Mark Carney said this month that such a reference rate should in future be based on actual market transactions and not banks' judgements.
Andrew Bailey, chief executive of the Financial Conduct Authority, told an event in London on Thursday that work must "begin in earnest" on shifting to an alternative index, saying the end of 2021 would offer time to ensure a smooth transition.
"By having a date by which transition will need to be complete, however, we give market participants a schedule to plan to, and make it easier for them to engage as many counterparties and Libor users as is practicably possible."
"In our view it is not only potentially unsustainable, but also undesirable, for market participants to rely indefinitely on reference rates that do not have active underlying markets to support them," Bailey said.
Banks have voluntarily agreed to keep contributing to Libor until 2021, but if this phase-out deadline was on course to be missed, there would be a "push" from the authorities, Bailey said, without elaborating.
At least six bankers on both sides of the Atlantic have been sent to prison for manipulating Libor, although some in the United States are still awaiting sentencing.
Libor had been compiled by the now defunct British Bankers' Association, but following the rigging scandal, this was transferred to ICE Benchmark Administration (IBA), part of the Intercontinental Exchange.
ICE had no immediate comment on the FCA's announcement.
The BoE has already been refining its overnight sterling funding rate SONIA, which is based on actual transactions and therefore seen as "near risk-free" and harder to manipulate, as a sterling Libor substitute.
Setting a date would focus minds in the same way that setting an end-2017 deadline to phase out Switzerland's TOIS reference rate triggered serious work on moving to the new SARON rate, he added.
The Federal Reserve is developing a home-grown benchmark based on the repurchase agreement or repo market as an alternative to dollar Libor, which is used in around $150 trillion of private and exchange-traded derivatives.