Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks

Abstract

Interest rate benchmarks are currently undergoing a major transition. The LIBOR benchmark is planned to be discontinued by the end of 2021 and 'replaced' by what ISDA calls an adjusted risk-free rate (RFR). ISDA has recently announced that the LIBOR 'replacement' will most likely be constructed from a compounded running average of RFR overnight rates over a period matching the LIBOR tenor. This new backward-looking benchmark is markedly different when compared with LIBOR. It is measurable only at the end of the term in contrast to the forward-looking LIBOR, which is measurable at the start of the term. On the other hand though, RFRs provide a simplification because the cash flows and the discount factors may be derived from the same discounting curve, thus avoiding--on a superficial level--any multi-curve complications. We develop a new class of savings account models and derive a novel interest rate system specifically designed to facilitate a high degree of tractability for the pricing of RFR-based fixed-income instruments. The rational form of the savings account models under the risk-neutral measure enables the pricing in closed form of caplets, swaptions and futures written on the backward-looking interest rate benchmark. An interesting twist is that the proposed rational savings account models are different from so-called short rate models in that they cannot necessarily be expressed as an exponentiated integral of a short rate of interest.

Keywords: LIBOR, SOFR, SONIA, Rational Term Structure Models, Swaptions, Caplets, Futures.

JEL Classification: C22, C60, G12, G13