Modeling SOFR and Fed Funds Short-Rate Dynamics

Summary

This paper presents a term-structure model designed for a market where SOFR is a central US dollar risk-free benchmark and overnight rates are key observable inputs. It emphasizes empirical features that longer-maturity-rate models may overlook, including the connection between SOFR and the Effective Federal Funds Rate, which is closely influenced by monetary policy decisions.

The model accounts for jumps in overnight rates around scheduled Federal Open Market Committee meetings, while forward rates implied by SOFR and Fed Funds futures continue to evolve diffusively. It is calibrated to futures prices and reconciles those forward-rate dynamics with a target short rate that follows piecewise constant paths. This framework is relevant to modeling rate expectations and futures pricing. The document provides no calibration results, parameter estimates, or comparison with alternative models, so it does not establish predictive accuracy or trading profitability.

Key ideas

• SOFR's role as a dollar risk-free benchmark motivates term-structure models that use overnight-rate behavior.
• SOFR and the Effective Federal Funds Rate are linked, and both can jump at scheduled policy meeting dates.
• Futures prices reflect market expectations of these policy-related rate changes.
• The model combines diffusive forward-rate dynamics with a piecewise constant target short rate.
• The paper calibrates the model to SOFR and Fed Funds futures prices.

Tags

# Short Rate Dynamics: A Fed Funds and SOFR perspective


# Short Rate Dynamics: A Fed Funds and SOFR perspective









The Secured Overnight Funding Rate (SOFR) is becoming the main Risk-Free Rate benchmark in US dollars, thus interest rate term structure models need to be updated to reflect the key features exhibited by the dynamics of SOFR and the forward rates implied by SOFR futures. Historically, interest rate term structure modelling has been based on rates of substantially longer time to maturity than overnight, but with SOFR the overnight rate now is the primary market observable. This means that the empirical idiosyncrasies of the overnight rate cannot be ignored when constructing interest rate models in a SOFR-based world. As a rate reflecting transactions in the Treasury overnight repurchase market, the dynamics of SOFR are closely linked to the dynamics of the Effective Federal Funds Rate (EFFR), which is the interest rate most directly impacted by US monetary policy target rate decisions. Therefore, these rates feature jumps at known times (Federal Open Market Committee meeting dates), and market expectations of these jumps are reflected in prices for futures written on these rates. On the other hand, forward rates implied by Fed Funds and SOFR futures continue to evolve diffusively. The model presented in this paper reflects the key empirical features of SOFR dynamics and is calibrated to futures prices. In particular, the model reconciles diffusive forward rate dynamics with piecewise constant paths of the target short rate.

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