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Modeling the Effective Fed Funds Rate and Its Derivatives

Article Quant Q&A · Author: MikeRand
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Summary

The document considers whether practitioners use a standard model for the Effective Federal Funds Rate, particularly one that captures policy-driven jumps around Federal Open Market Committee meetings. It contrasts this daily overnight rate with term LIBOR, whose longer tenor makes it less directly sensitive to individual meeting dates, and asks whether short-rate models or an HJM-style framework are more appropriate.

The answer says that Fed Funds derivatives were predominantly linear forwards, reducing the need to model the full daily rate distribution precisely. It notes that the larger market in three-month LIBOR derivatives had supported more extensive modeling, and suggests that daily-step HJM methods could become relevant as markets shift toward overnight benchmarks such as Fed Funds and SOFR. A second answer points to research on shadow rates for several economies. The material is a brief, historically situated discussion, not a consensus specification: it gives no model equations, calibration method, or evidence that the proposed approach became standard.

Key ideas

  • The document reports that Fed Funds derivatives were mainly linear forwards, limiting demand for detailed distribution models.
  • Daily policy-rate moves make Effective Fed Funds more sensitive to FOMC meetings than term LIBOR.
  • A daily-step HJM-style framework is suggested as a possible approach for overnight rates.
  • The discussion is historically situated and does not establish a standard model or provide calibration details.

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Fixed incomeDerivatives pricingStatistics
Full text
# "Standard" Model for Effective Fed Funds Rate


# "Standard" Model for Effective Fed Funds Rate












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?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/42501

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.

## Answer by Lars Pellarin (score 1)

https://quant.stackexchange.com/a/41581

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.