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.
Highlights
London interbank offered rate (LIBOR)-based derivatives market as an indicator, one would expect risk-free rate (RFR) linked versions of swaps, caps and swaptions along with the already trading Secured Overnight Financing Rate (SOFR)/Sterling Overnight Index Average (SONIA) futures to become liquid once LIBOR has been discontinued
This is what International Swaps and Derivatives Association (ISDA) refers to as the Risk-Free Rate (RFR), a benchmark rate that may correspond to SOFR, SONIA, Euro Short-Term Rate (eSTR) etc., in their respective currencies
In this paper we develop a new class of rational term structure models that is tailored to the new backward-looking interest rate benchmarks, which are meant to supersede the forward-looking
Summary
Since the speech of Andrew Bailey, the Chief Executive of the Financial Conduct Authority, in 2017 on the future of the London interbank offered rate (LIBOR) it has steadily become clearer that the LIBOR interest rate benchmarks are no longer going to be supported in several major currency denominations. LIBOR-based derivatives market as an indicator, one would expect RFR linked versions of swaps, caps and swaptions along with the already trading SOFR/SONIA futures to become liquid once LIBOR has been discontinued. In this paper we develop a class of discounting models that allows for closed-form pricing of derivatives written on a backward-looking benchmark. It is motivated by the recent work of Mercurio (2018) and Lyashenko and Mercurio (2019). Most of the rational term structures models allow for closed-form swaption pricing, but—as we will show—these models are not well-suited for modelling a backward-looking benchmark. We wrap up with concluding remarks and an outlook on future investigations
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