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Looking forward to backward‑looking rates

Looking forward to backward-looking rates

Interbank offered rates (Ibors) are critical in the world of contracts and derivatives, acting as reference rates in millions of financial contracts and with a total market exposure in the hundreds of trillions of dollars. Bloomberg explores why offering effective and efficient solutions is pivotal for a successful transition away from Libor

Investors can see the expiration of Libor in 2021 rapidly approaching. The pillars of new risk-free rates (RFRs) are being raised and practical architecture built around them. An industry practitioner and academic focused on rates and markets, Fabio Mercurio, global head of quantitative analytics at Bloomberg and adjunct professor at New York University, shared his thoughts on Libor replacement at a recent Bloomberg Quant seminar. Mercurio has written extensively on topics in quantitative finance and risk, including in his recent paper, co-authored with Andrei Lyashenko.

Ibors play a significant role in the world of contracts and derivatives, serving as reference rates in millions of financial contracts, with a total market exposure exceeding hundreds of trillions of dollars. Thus, effective and efficient solutions are essential for migration to the post-Libor environment.

As regulators, industry organisations and market participants have been developing an alternative framework for new benchmarks, a number of solutions have emerged: the US is working with the secured overnight financing rate (SOFR), the UK with a reformed sterling overnight index average (Sonia), Switzerland has selected the Swiss average overnight rate (Saron), the Tokyo overnight average rate (Tonar) in Japan and the eurozone has adopted the euro short-term rate (€STR), which it plans to start publishing in October 2019.


Seeking substitutes for Ibors

All of these RFRs are overnight rates and must be converted into term rates before they can serve as substitutes for Ibors in any kind of contract, new or old. To ensure a smoother transition, the International Swaps and Derivatives Association and regulators are looking at two main approaches:

  • A compounded, backward-looking, setting-in-arrears rate, which will be known at the end of the corresponding application period
  • A market-implied prediction of this rate, which is then forward-looking and known at the beginning of the application period.

In the current environment, the backward-looking rate was chosen as the RFR term rate in the definition of the Libor fallback for derivatives and is seen in new RFR futures and vanilla swaps, for example. The forward-looking rate seems to be preferred in defining fallbacks for cash instruments. But some may ask: “Is there a way to unify these two worlds?” Mercurio and Lyashenko have developed a modelling framework where the backward- and forward-looking rates can be modelled jointly. As they have shown, it does not matter if some contracts use the first rate and others use the second, as it is possible to have a framework that accommodates both.

Their work in this area focuses, in part, on defining and modelling forward RFRs, based on the new interest-rate benchmarks that will be replacing Ibors globally. By modelling the dynamics of term rates directly, it is possible to simulate the forward-looking Ibor-like rates and the backward-looking setting-in-arrears rates using a single stochastic process for both varieties. This leads to what is known as a generalised forward-market model (FMM), which is an extension of the classic single-curve Libor market model (LMM), with the benefit of the FMM providing additional information about the rate dynamics between fixing and payment times.

The FMM formulation is based on the concept of extended zero-coupon bonds – useful when handling backward-looking setting-in-arrears rates. With such an approach, bonds, forwards and swap rates – along with their associated forward measures – can all be defined at all times, even beyond their natural expiries.

As the market continues to develop alternatives to Libor, the FMM is a noteworthy development that offers several advantages over the classic LMM and can be further enhanced by adding Libor-like rates in a process described in one of Mercurio’s earlier papers. In this way, a multicurve model can be constructed through modelling RFR term rates jointly with forward Libors or Libor proxies. The FMM is not an alternative to the LMM, but rather an extension of it – compatible with the new RFR term rates chosen as Libor replacements. While the sun is setting on Libor, it will rise again with insightful market innovation.



Libor transition and implementation – Special report 2019
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