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It looks like LIBOR is set to be phased out at the end of 2021.

Why is this happening?

This PwC representative says that banks don't really use LIBOR that much, and the new "alternative rate" system will better reflect the real interest rates paid by banks to each other.

How is this alternative system going to work and how will it impact all the derivatives that currently depend on LIBOR, such as the Eurodollar futures contract?

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Libor is being phased out because of the Libor scandal. According to a USA today article from 2012

Some banks artificially inflated or deflated their rates, depending on what would benefit them most. Some may have deflated their rates to give the impression that they were more creditworthy than they actually were.

The Bank of England is transitioning to an alternative risk free rate system based on the SONIA benchmark.

SONIA is based on actual transactions and reflects the average of the interest rates that banks pay to borrow sterling overnight from other financial institutions.

Since SONIA is based on what banks actually pay rather than what they say they might, in theory pay, it's less easy to manipulate.

The transition has taken a long time because banks and other institutions created a lot of contracts that referenced Libor, including the Eurodollar futures contracts that you mention, and it's taken a long time to identify all of these contracts, rewrite them and get everyone to agree to each new contract. This is called the Libor repapering challenge

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