  The LIBOR rate is currently scheduled for discontinuation, 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 dynamic arbitrage-free models for the SOFR term
structure. The models allow you to construct forward-looking SOFR term rates,
imply a SOFR discounting curve and price and risk and risk manage SOFR
derivatives, not yet liquidly traded in the market. We find that a standard
three-factor Gaussian arbitrage-free Nelson-Siegel model describes term rates
very well but a shadow-rate extension is needed to describe the behaviour near
the zero-boundary. We also find that the jumps and seasonal effects observed in
SOFR, do not need to be specifically accounted for in a model for the futures
prices. Finally we study the so-called convexity correction and find that it
becomes significant beyond the 2 year maturity. For validation purposes we
demonstrate that our model aligns closely with the methodology used by the
Federal Reserve to publish indicative SOFR term rates.
