Updated publication: ERIS futures: Analysis and pricing

We are pleased to announce an updated working paper titled

ERIS futures: Analysis and pricing

is available in our muRis_Q Advisory Instrument Analysis series of research papers. The paper is available on SSRN preprint repository at http://ssrn.com/abstract=5666790.

This version contains an update from the October 2025 version which refers to a previous setting mechanism for the daily settlement price. The author thanks ERIS Innovation for providing the basis data discussed in Section 4.3 and useful discussions on the product details.

Abstract

In this note we describe ERIS futures and propose a pricing mechanism for them. Those futures are swap futures associated with OTC cleared swaps. We come to the conclusion that the claim that they ``replicate cash flows of OTC swaps'' is reasonable in theory in the context of the multi-curve framework. The daily settlement price is based on a valuation curve calibrated using a mixture of end of day futures prices and external data. Based on the anchoring of the prices on the short term to SOFR futures and OTC swaps, the replication claim appears also reasonable in practice. We also analysed the possibility of having fully standalone instruments; for that part, our answer is more prudent and mainly negative.

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Don't hesitate to contact us if you require advisory services related to the interest rate modelling or benchmark transitions.

Multi-curve framework: book and workshops

The publication of the second edition of Marc's book, "Interest Rate Modelling in the Multi-Curve Framework" is getting closer (see details on Marc's blog: https://multi-curve-framework.blogspot.com/p/details.html).

To support the implementation of the framework, we are offering customised in-house workshops. These sessions focus on:  Practical Implementation: Moving from theory to practice. Collateral Integration: Understanding the complex interplay between CSA terms and discounting. Calibration: Available instruments, basis spreads, cross-currency.

The typical training agenda is available here, but we are happy to adjust the content to meet your specific needs. The usual audience are traders, quants, model validators and risk managers who want to understand the foundation of the framework. For questions regarding potential course content, don’t hesitate to contact us.

There will also be some public courses. A 2-day course is planned.

Interest Rate Modelling in the Multi-curve Framework:
Foundations, Evolution, Transition, and Implementation

Warsaw on 18-19 May (see brochure).

The "local" price (PLN 5800) is for the course and lunches. For "international" participants, there is the possibility to include 2 nights accommodation in Bristol Hotel (course, accommodation at Bristol with breakfast, 2 x coffee breaks and lunch during the training; subject to availability) at 1650 EUR/per person. No prepayments (only official registration needed, invoice sent after the training; no VAT tax for EU members). For practical questions regarding the organisation and price of Warsaw’s course, you can contact Tomasz DENDURA

New muRisQ’s corporate swag

You may remember our golf ball collection, starting with this.

We now have a new load with our logo.

Don't hesitate to ask for a sleeve!

New publication: ERIS futures: Analysis and pricing

We are pleased to announce a new working paper titled

ERIS futures: Analysis and pricing

is available in our muRis_Q Advisory Instrument Analysis series of research papers. The paper is available on SSRN preprint repository at http://ssrn.com/abstract=5666790.

Abstract

In this note we describe ERIS futures and propose a pricing mechanism for them. Those futures are swap futures associated with OTC cleared swaps. We come to the conclusion that the claim that they ``replicate cash flows of OTC swaps'' is reasonable in the context of the multi-curve framework. Currently their daily price settlement is based on a third party valuation and the futures are not standalone with prices based on actual futures trades. We also analysed the possibility to transform them into standalone instruments with price obtained from recent trade information. For that part, our answer is more prudent and mainly negative in large part due to the lack of liquidity along the curve.

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Don't hesitate to contact us if you require advisory services related to the interest rate modelling or benchmark transitions.

SOFR and EFFR are getting excited!

For some time, we have reported about the volatility of the SOFR / target spread in the USD market (see for example SOFR is getting more alive!). Today we can even report on some volatility of the EFFR / target spread!

The news has even reached the main newspapers like the Bloomberg and Financial Times.

The EFFR has been at target plus 8 bps for several years. Only in the last months was there some volatility, with the spread going up to 12 bps. The target rate targets the EFFR, in that sense we can say that the targeting has been very effective. But in reality it sounds like a self fulfilling prophecy. The volumes are quite small (see below) and the number of participants restricted. The bid/offer implied by the 25/75 percentile is 1 bp, not a realistic number for a real cash market.

When comparing with the overnight repo market represented by SOFR, one can see the difference with a “real” market. Bid-offers are in the 10 to 15 basis points and the rates change each day. There are patterns, in particular at month-end, but also you can see the market stresses.

Figure 1 and Figure 2 represent the spread between the different rates and the lower bound of the target range. In Figure (1) the date since January 2023 is represented and in Figure 2, the focus is on the year 2025.

Figure 1: Spread over target rate for SOFR and EFFR benchmarks. Data since January 2023.

Figure 2: Spread over target rate for SOFR and EFFR benchmarks. Data since January 2025.

In the graphs, we have also added the Interest On Reserve Balance (IORB), which is the interest that banks receive from the Federal Reserve for balances in their account. Since 2021, there is no distinction between the mandatory reserves and the excess reserves, all of them receive the same interest. Since that date, it has always been at Target plus 15 basis points.

Given the lack of movement in the EFFR / Target spread, it has been suggested that the Target should maybe be changed to SOFR (Options for modernizing the FOMC’s operating target interest rate). Even some Federal Reserve (of Dallas) economists acknowledge that the EFFR are not really “effective” anymore by indicating “interbank loans are far less important to the financial system than they once were” and “connections between the fed funds market and broader money markets have grown fragile”.

This leads us to the volumes underlying the two main overnight indices in the US market displayed in Figure 3. As can be seen in the graph, the volume underlying EFFR has been roughly unchanged, around 100 billion USD a day, for a long time. Over the last 3 years, the volume underlying SOFR has increased steadily from 1,000 to 3,000 billion USD a day.

Figure 3: Volume underlying EFFR and SOFR since 2018.

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Don't hesitate to contact us regarding the modelling of overnight rates.

New book, special offer

Marc’s multi-curve framework book is expected to be available from November on. To celebrate the achievement, muRisQ is proposing a special offer. For each in-house course related to the multi-curve framework, a book copy is offered to each participant. A typical agenda for such a course can be found on our training page.

As usual the course agenda will be tailor made to your needs.

More information on the book can be found on Marc’s blog at https://multi-curve-framework.blogspot.com/p/details.html.

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Don't hesitate to contact us regarding interest rate modelling courses.

MVA: from derivatives to people

It appears that the US is planning to require some visitors to pay a bond of up to USD 15,000 for a visa.

Many political comments have been made about it; we would like to bring some light quant comments.

The term used for the visa is “bond”, in the market this type of requirement is called “Collateral” or “Initial Margin” (IM). The quantitative and valuation impacts of those IM requirements have been studied extensively in the literature with regard to derivatives and are known under the name MVA.

The mechanisms would be that the person requesting a visa would deposit a certain amount before using the visa and the amount would be returned when the person has departed the US.

Some parts of the mechanism are similar to IM, and thus require some MVA computations, some other parts are different and require further adjustments.

Some visas, including business visas, require a bond. This bond deposited during the length of the visa usage has some cost, for a corporation this is typically a funding cost. That means that any corporation making business with the US which requires visits from oversea staff will need to incorporate that cost to their prices. This is the MVA part.

By opposition to the standard IM practice in the OTC market, here the IM is deposited not with a third party custodian, but directly with the counterparty (the US government). On that amount there is a non-negligible credit and legal risk. What if the US defaults, or more likely refuses to pay the margin back? What for multi-entry visas? Can the US keep the bond up to the end of visa validity? What if the depositor died before claiming the amount back? Here the question moves from a MVA-like question to a CVA-like question. Involving probability of default (PD) and loss given default (LGD). The LGD may even be higher than 100% of the bond amount itself if the legal cost is added.

In all cases, corporations planning to make business with the US should analyse the potential cost of such a framework (this analysis is itself a cost). We are not experts in political risk, but we have helped clients with many Initial Margin methodologies.

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Don't hesitate to contact us regarding the impacts of initial and variation margin on derivative pricing.

Qu'est-ce qu'un Analyste Quantitatif ?

Après un début de carrière dans le monde académique, depuis 25 ans j’exerce comme “analyste quantitatif” – ou simplement “quant” dans le jargon financier. Mais qu’est-ce qu’un quant et que fait-il ? J’ai souvent du mal à l’expliquer à mes connaissances ; je voudrais essayer de le résumer ici. D’abord il existe plusieurs sortes de quants, les quants de valorisation de produits dérivés, les quants de big data, les quants de portefeuille d’investissement, etc. Je ne peux parler que de la première catégorie, celle à laquelle j'appartiens.

Ceci est l'introduction de l'article publié dans l'EcoFin MAG de juin 2025 dont Marc est l'auteur.

Un lien vers une version életronique est disponbile ci-dessous:

Qu'est-ce qu'un Analyste Quantitatif ?

Bonne lecture!

New muRisQ’s corporate swag

You may remember our golf ball collection, starting the one related to the publication of Marc’s book, you may have seen our branded polos and jackets, now we have also nice caps available!

Figure 1: A cap on top of Marc’s books!

Interest Rate Instruments and Market Conventions Guide - Post LIBOR edition

As announced previously, we have been working on the updated Interest Rate Instruments and Market Conventions Guide. We are glad to announced that the new version

Interest Rate Instruments and Market Conventions Guide - Post LIBOR edition

is now available. You can download it from SSRN at https://ssrn.com/abstract=5099269.

Comments on the content - typos, missing indices, new products - are welcomed.

The benchmark page on our web site has a list and short descriptions of (some) overnight and IBOR-like benchmarks available at

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

We will do our best to maintain it up-to-date.

SOFR is getting more alive!

In a blog post a couple of month ago, we noticed that “SOFR is really alive again!” After several years of manipulation by the Federal reserve, the benchmark was showing signs that it was actually reacting to market developments.

It appears that those life signs are increasing. In Figure 1 we propose the graph of the SOFR and EFFR spread above target rate over a two-year period. The coming alive of SOFR is clearly visible.

Figure 1: Spread over target rate for SOFR and EFFR benchmarks.

If we look at SOFR’s and EFFR’s average spread (in bps) above target we have

Period	SOFR	EFFR	Note
2023	5.95	7.92
2024	8.14	8.00	EFFR=8bps every day
2024-H2	9.61	8.00

What does the market think about the above SOFR features? For that we looked at the forward SOFR-EFFR spread as quoted in the USD OIS market. Figure 2 displays data on the above spread for OISs with tenor 1, 10, and 30 years. The spreads are for SOFR + spread versus EFFR. A negative spread, as most of the time in the last two years, indicates that the market is ready to pay more for SOFR than for EFFR.

Figure 2: Spread for OIS basis swaps: SOFR + spread V EFFR.

SOFR is a secured rate while EFFR is unsecured. The two pieces of information above, the realised rates over the last 6 months and the forward looking market spreads, indicate that a secured rate is higher than an unsecured rate! We are quantitative finance advisors, not economical advisors; but the laymen in us thinks that “something is rotten in the State of Benchmark (Federal Reserve provided)”.

Moreover, at the view of Figure 1, the Fed sanctioned method to interpolate the SOFR curve described in Heitfield and Park (2019) and used in CME futures based SOFR Term rate, is less and less credible. Saying that the Fed has a biased view of the impact of the Fed on the market may not be a surprise.

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Heitfield, Erik, and Park, Yang-Ho (2019). “Inferring Term Rates from SOFR Futures Prices,” Finance and Economics Discussion Series 2019-014. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2019.014.

Cross-currency basis futures

CME is planning to launch a futures contract related to the OTC cross-currency basis between USD-SOFR and EUR-ESTR. The futures is cash settled against a proprietary cross-currency index. muRis_Q is proposing a note proposes describing the index and the associated futures. The links and differences between the index, the futures and the OTC market is analysed.

Marc's Market Infrastructure note is available at:

Cross-currency basis futures: description

The analysis of the fixing basis and the convexity adjustments will be proposed in a forthcoming muRis_Q Model Development instalment.

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Don't hesitate to contact us regarding the pricing or risk management of interest rate and forex products.

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.