A perpetual FRN which contains a call option given to the issuer. However, if the issuer doesn’t exercise this option during a specific period of time (say, 5 years), then the spread over the reference rate would widen. For example, if the floating rate is determined as LIBOR plus 100 basis points, then, if the option is not exercised within the specified period, the floating rate readjusts to LIBOR plus 250 basis points. Fake perpetual FRNs are usually issued by banks that need capital in the form of subordinated debt. These instruments help to raise perpetual capital, though perpetuity is unlikely, but remains possible.
A fake perpetual FRN is also known as a fake perpetual floater.
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