Rational Savings Account Models for Backward-Looking Interest Rate Benchmarks

• Main Authors: Andrea Macrina, David Skovmand
• Format: Article
• Language: English
• Published: MDPI AG 2020-03-01
• Series: Risks
• Subjects: libor; sofr; sonia; libor transition; risk-free rates; rational term structure models; swaptions; caplets; futures
• Online Access: https://www.mdpi.com/2227-9091/8/1/23

Interest rate benchmarks are currently undergoing a major transition. The LIBOR benchmark is planned to be discontinued by the end of 2021 and superseded by what ISDA calls an adjusted risk-free rate (RFR).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. The RFR provides 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.