SOFR term structure dynamics—Discontinuous short rates and stochastic volatility forward rates

The Secured Overnight Funding Rate (SOFR) has become the risk-free rate benchmark in US dollars, thus term structure models should reflect key features exhibited by SOFR and forward rates implied by SOFR futures. We construct a multifactor, stochastic volatility term structure model which incorporates these features. Calibrating to options on SOFR futures, we achieve a reasonable fit to the market across maturities and strikes in a single model. This also provides novel insights into SOFR term rate behavior (and implied volatilities) within their accrual periods, and a model mechanism by which interest rate mean reversion arises from monetary policy.