Short Rate Dynamics: A Fed Funds and SOFR perspective

Abstract

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 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. † The authors thank Leif Andersen for helpful comments on a previous draft of this paper. The usual disclaimers apply.

Dynamic Term Structure Models for SOFR Futures

“…But the existing approaches have mainly focused on pricing derivatives on the compounded SOFR average, and have not taken their models to actual data. An exception is Gellert and Schlögl (2021), that perform a multi-date calibration under the risk-neutral measure with a view towards analyzing the impact of SOFR spikes.…”