Dynamic Term Structure Models for SOFR Futures

Abstract

The LIBOR rate is currently scheduled for discontinuation by the end of 2021, and the replacement advocated by regulators in the US is the Secured Overnight Financing Rate (SOFR). The change has the potential to disrupt the \$200 trillion market of derivatives and debt tied to the LIBOR. The only SOFR linked derivative with any significant liquidity and trading history is the SOFR futures contract, traded at the CME since 2018. We use the historical record of futures prices to construct a dynamic arbitrage-free model for the SOFR term structure. The model allows you to construct forward-looking SOFR term rates, imply a SOFR discounting curve and price and risk manage SOFR derivatives, not yet liquidly traded in the market. We find that a three-factor Gaussian arbitrage-free Nelson-Siegel model is particularly well suited for the SOFR futures market. For validation purposes we demonstrate that our model aligns very closely with the model-free methodology used by the Federal Reserve to publish indicative SOFR term rates.

Keywords: SOFR, LIBOR, Futures, Arbitrage-Free Nelson-Siegel, Term Structure Models

JEL Classification: G13