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I understand LIBOR rates quoted on a daily basis upto 12 M tenors. But how are rates beyond 12M tenor estimated. I got this question from an interviewer.

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If you want to estimate interbank lending rates beyond 12 months, the best you can do is look at where bonds issued by banks are trading.

Sometimes there is loose talk (even by interviewers) that may confuse this with long term swap rates, which are contracts to exchange a fixed rate for 3 or 6 month libor. However this has nothing to do with bank lending beyond 12 months.

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