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Is there a "standard" model used to model the Effective Fed Funds Rate? I know that BGM is often used for LIBOR but haven't found a similar application to the Effective Fed Funds Rate.

Do practicioners just use short rate models even though they don't accurately reflect the jumps in the target rates at FOMC meeting dates, or is there another HJM-type model used for the Effective Fed Funds rate?

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In practice, most derivatives traded on Fed Funds rates are linear(i.e. Forwards) rather than non-linear (options and exotics). As such, there has not been a strong case for precise modeling of the full distribution of a Fed Funds rate for a particular day. In contrast , there is a large market for derivatives on 3month USD Libor , which is less sensitive to FOMC meeting dates because it is a 90 day term rate. Hence short rate models may be ok for modeling Libor.

With Libor's demise scheduled for 2021, quants may need to refocus on modeling daily rates such as Fed Funds and SOFR, the Secured Overnight Financing Rate, which has been chosen as the replacement rate for Libor. A HJM-style model with daily time steps may be a candidate.

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Wu and Xia did some interesting work with modelling the effective EU, US and UK interest rates https://sites.google.com/site/jingcynthiawu/home/wu-xia-shadow-rates

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