  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.
