SOFR Term Structure Dynamics - Discontinuous Short Rates and Stochastic Volatility Forward Rates

Abstract

As more and more jurisdictions transition from LIBOR-type interest rate benchmarks to new riskfree rate (RFR) benchmarks based on overnight rates, such as SOFR in the US, it is important to adapt interest rate term structure models to reflect this. In particular, overnight rates are largely driven by monetary policy and thus display dynamics that are (at least to first order) piecewise constant between central bank rate decisions, while forward rates continue to evolve in a more diffusive fashion. We construct a tractable multifactor, stochastic volatility term structure model which incorporates these features. Calibrating to prices for options on SOFR futures, we achieve a good fit to the market across available maturities and strikes in a single, consistent model. The model also provides novel insights into SOFR term rate behaviour (and implied volatilities) within the SOFR term rate accrual periods, as well as into empirical mean reversion dynamics.

Keywords: SOFR, EFFR, Fed Funds, interest rate term structure modelling, interest rate futures, interest rate options

JEL Classification: G13, G18, E43