Workshop on multi-curve framework - Warsaw - 5/6 December 2024

Marc will present a two-day workshop on multi-curve framework on 5 and 6 December in Warsaw.

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More details can be found on the LinkedIn page related to the workshop. There are still seats available for that workshop organised by CEETA.

Et tu, ESTR!

In previous blogs, we reported the return of the month end SOFR volatility with regular increase of the spread above Fed Fund target. We have updated the graph and the data. As seen in Figure 1, the month-end volatility continues to be visible almost every month with a larger impact at the latest quarter end.

Figure 1: Spread over target rate for overnight benchmarks.

Over the reported period the average spreads of “normal” days are 7.08 bps. We report below the average spread above that average for “special” days:

Day of the month	Spread (bps)
1st	4.20
2nd	2.35
15th	0.30
Last	3.15

Based on our blog and presentations, it is natural to ask if something similar exists in other currencies. We have run an analysis for EUR. There the results are somehow the opposite. The last days of the month usually see a lower rate. This is reported in Figure 2. The numbers reported are the difference between the last business day of the month rate and the average of the two adjacent rates (second last day of the month and first day of the next month). The average decrease of rate is 1.13 bps with all month but one lower.

Figure 2: ESTR decreased rate at month end.

Benchmark page on our site

One very useful document related to interest rate market is Marc’s “Interest Rate Instruments and Market Conventions Guide". Its latest version was published more than 10 years ago as an OpenGamma Quantitative Research document. It can be found on SSRN at https://ssrn.com/abstract=2128257.

Over that time interval the interest rate market conventions have changed, in particular in relation to benchmarks. We are planning to update the guide and we will post here a link to the new version.

In the mean time we have added a benchmark page on our web site with a list and short descriptions of overnight and IBOR-like benchmarks: https://murisq.blogspot.com/p/conventions.html. We will do our best to maintain it up-to-date.

Don't hesitate to contact us if you think there are "glitches" in the list or to propose new information.

AMERIBOR is also alive!

A couple of days ago, we published a blog titled "SOFR is really alive again!" showing the return of (small) volatility of the SOFR spread above the Target rate. This small volatility was opposed to the dead spread of EFFR.

A natural question at the reading of the blog has been "What about AMERIBOR?".  The third overnight benchmark in the USD market is more directly linked to the actual deposit market without manipulation. 

The spread of AMERIBOR above the target rate is reasonably volatile. A graphical representation is proposed below.

Figure 1: Spread over target rate for three USD overnight benchmarks.

SOFR is really alive again!

In a post titled "Is SOFR alive again?" a couple of month ago, we were wondering if the month-end and mid-month volatility of SOFR was back or if it was only a temporary effect linked to the year-end. The answer seems to be that the month-end effect is really there again but the mid-month effect not.

The effect is represented graphically below. The graphs displays the spreads between the 2 main overnight rates in USD (EFFR and SOFR) and the US Target rate lower end of the range. The EFFR rate does not show any variation at 8 bps every day. The SOFR is usually slightly lower at 6 or 7 bps, but around month-end shows "burst" up to 15 bps.

Figure 1: Spread over target rate for overnight benchmarks.

Over the last 10 months displayed in the above figure, the mean spread for the “rest” bucket is 6.48 bps. For the other periods, we measured the spread above that mean (i.e. spread of spread). The results are

Day of the month	Spread (bps)
1st	3.32
2nd	2.32
15th	-0.10
Last	2.08

The feature should probably be incorporated into the SOFR curve calibration when dealing with large volume of SOFR-linked products (OIS, CSA collateral, SOFR futures, etc.). A mechanisms to incorporate this feature in curve calibration is proposed in Chapter 5 of Marc's multi-curve framework book (note: a new version is in progress).

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Note that CME SOFR term rates do not include this feature in their "interpolation" mechanism. The CME SOFR term rates are probaly not fully suitable for precision hedging of the SOFR risk.

New offices: work (almost) in progress

muRis_Q Advisory is happy to announce the launch of the work on its new offices.

The new offices will be located in the municipality of Namur in a building of the late 19th century. The heavy work will start in October.

The offices will be divided in two parts: a “communication office” and a “research and development office”. The former will be used for client reception and online meetings. The latter will be organised as a library with reading desks and large bookshelves with relevant quantitative finance, mathematics, computer science and economic literature.

We will post pictures of the new premises once the transition is over.

The new office's floor plan

Marc's multi-curve book: new edition in progress

It has been 10 years since Marc published the first edition of his book Interest Rate Modelling in the Multi-Curve Framework: Foundations, Evolution and Implementation. He is now preparing a new edition as announced on his personal blog:

https://multi-curve-framework.blogspot.com/2024/04/multi-curve-book-new-version-in-progress.html

As a preview of the book, we have created a new page on muRis_Q Advisory site with the content of the "convention" appendix.

The page is available at:

https://murisq.blogspot.com/p/conventions.html

Is SOFR alive again?

The title may sound prosperous as SOFR as been the main benchmark in USD interest rate (at least in term of PV01) for more than six months.

SOFR has been manipulated (Note: "manipulate: to use something, often with a lot of skill", Cambridge Dictionary ) by the Federal Reserve Bank by intervening in the repo market, up to USD 1,000 billions a day. If you go back to the last quarter of 2019, there were large variations in SOFR between the “normal” days and the days influenced by government actions (month end for balance sheet measurement and 15th of the month for tax payments). After the Fed interventions, the market impact of those influences disappeared; the public sector compensated one intervention by another.

This blog title refers to that “life” of SOFR, its reaction to external influences. In 2019 we proposed a blog on how to include that seasonal life into curve calibration. After a couple of years where the SOFR daily reading (above the Fed target rate) were completely flat, there has been a little bit of action over the last months. Figure 1 represents the spread of overnight benchmarks (SOFR and EFFR) above the target rate. EFFR is completely flat at 8 bps. SOFR shows more life. The days have been divided in a certain number of buckets: 1st (business) day of the month, 2nd day of the month, 15th of the month, last day of the month, (overnight period containing the mentioned dates) and the rest.

Figure 1: Spread over target rate for overnight benchmarks.

Over the last 6 months displayed in the above figure, the mean spread for the “rest” bucket is 6.42 bps. For the other periods, we measured the spread above that mean (i.e. spread of spread). The results are

Day of the month	Spread (bps)
1st	2.92
2nd	2.75
15th	0.08
Last	2.08

There is indeed some impact around month-end/start. It is largely impacted by year end. We will see if the impact continues through the year.

Quant Insights Conference - Seminar

Marc will present at the Quant Insights Annual Conference on 1 November 2023 (free online tickets available).

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Marc's presentation will be based on his recent paper

Bond futures: Delivery Option with Term Structure Modelling

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Don't hesitate to contact us if you you are interested by implemented this approach or other term structure modelling.

LIBOR derivative volume in absence of LIBOR fixing

The post title may sound a little bit oxymoronic. It is not the fault of this author but the fault of the regulators and the market…

Derivatives are split in different categories: ETD, OTC cleared and OTC uncleared. The meaning of “LIBOR” in each of those categories is different and is also different from LIBOR fixing. This usage of the same name to describe different things is the source of the confusion in the post’s title.

Note that this usage of “same name; different things” description is fundamentally different to the

Mathematics is the art of giving the same name to different things.

Henri Poincaré

Poincaré meant different things with the same properties, to which similar truths can be applied. Here we have things that should be the same in a decent world but have different properties and to which different (legal) truth apply.

LIBOR fixing in USD have ceased as of 30 June 2023 (not really ceased, but that will discussed later).

The ETD derivatives went through a forced (arbitrary) conversion well ahead of the milestone date (on 14 April 2023 for CME). They have completely disappeared and are not the subject of this post.

The OTC uncleared derivatives are mainly traded under ISDA master agreement. We discuss only those here. The derivatives traded before January 2021 had uncertain fallback mechanisms under the ISDA definitions, or more exactly, there is a certain fallback mechanism (call 4 baks for indicative LIBOR quotes) but it is certain that the mechanism cannot be implemented in practice. Some of those derivatives have been transferred, through a protocol mechanism, to fall under the post January 2021 definitions; this case is described below.

The pre January 2021 do not yet have a legal issue, because LIBOR fixing still exists! This may seem in contradiction to the post title that claim an absence of LIBOR fixing; but again this is a contradiction only because the same name is used for different things (again not in the Poincaré sens). Maybe we will be in trouble with EU Digital Service Act (DSA) that may try to censure this as “disinformation” or “misinformation”!

The “true” LIBOR, representing the interbank lending rate, as ceased on 30 June 2023. But a “fake” LIBOR fixing has been imposed by the regulator, the FCA. This LIBOR is based on an arbitrary formula replacing the market based definition in use since 1986. The regulator imposing an arbitrary definition for a critical benchmark is possible thanks to post-Brexit change of the UK BMR regulation, in particular Article 23A. That change gives the super-power to the regulator to change a benchmark definition. If tomorrow you see that the temperature in London 20 degree Celsius for the while month of the December, this is most likely not a result of the climate changes but a result of the FCA decision to change the meaning of “temperature”. This “fake” LIBOR should stop on 28 March 2024. We will only see then the true legal impact of the transition on USD LIBOR OTC derivatives (and bonds, and loans, and structure products).

The post January 2021 trade do not have a problem either, because ISDA forced a “non-representative” clause in the new definition. The LIBOR trade do not reference LIBOR anymore, even if LIBOR still exists. This is because the regulator that have created a new definition for LIBOR have immediately declared that what they have created is not representative of the market it is suppose to represent — while the previous version was representative. Those trades have been converted to SOFR-linked derivatives that are not really OIS (see fallback transformers and subsequent posts). Unfortunately, there is no detailed public information about the volumes of those; we can not report on it.

We come to the next type: OTC cleared. For that category, some data is available and we describe below some figures from LCH.

The existing LIBOR swaps have been converted to SOFR swaps. The conversion has been done but spliting the existing swaps in 2, one LIBOR part that continues to the last payment of the LIBOR fixed before 30 June and the SOFR part that starts after that. That conversion has been done mid-May 2023. Since that date, the outstanding LIBOR swaps have decreased from 48 trillions to 273 billions. The decrease is almost linear from the amount on the conversion date to 0 three months later. Most of the LIBOR swaps have a LIBOR-3M benchmark, hence that period. There is a little bit of 6-month tenors and 12-month tenors, so the small residual that continues to disappear.

Swaps linked to LIBOR continue to be cleared at LCH. From 3 July 2023 to 13 October 2023, roughly 400 billions of USD-LIBOR swaps have been cleared. Those swaps are most probably coming from USD-LIBOR swaption with physical exercise. This is a non-negligible amount for a non-existing benchmark. Those swaps are immediately converted to SOFR and do not enter into the outstanding amounts described in the previous section.

If we look at the total outstanding amount in USD, it decreased only by 9.3 trillions over the period, even with the 47.7 trillions of LIBOR swaps disappearing. This is somehow expected. The LIBOR swaps converted to SOFR-linked swaps are not standard OISs. So no direct offset between the converted swaps and the standard one is possible. It would be possible to eliminate them with some compression cycles, but not all participants are part of the those cycles.

Note that GBP, JPY an CHF LIBOR swaps (also coming from swaptions) are still cleared 22 months after the discontinuation of their respective LIBORs. The amounts (in USD equivalent) are GBP 1.330 billions, JPY 4.54 billions and CHF 0.17 billions.

There is also 13 trillions of outstanding basis swaps. With the disappearance of LIBOR, those basis are certainly SOFR v EFFR. The US SOFR RFR adoption indicator for September is down to 68.3% from 76.2%, another sign that EFFR is still playing an important role in USD derivatives.

The short conclusion is that LIBOR transition is still in progress even in the absence of LIBOR!