Monday 27 December 2021

ESTR, SOFR and SONIA - end 2021

There have been a lot of discussions around ESTR, SOFR and SONIA over the last years. The interest rate derivative market was quite symmetrical between those currencies up to a couple of years ago. The market was dominated by one IBOR benchmark (EUR-EURIBOR, USD-LIBOR, GBP-LIBOR) with a decent overnight benchmark (EUR-EONIA, USD-EFFR, GBP-SONIA).

The three currencies have used different paths in their benchmark transition. On the overnight side, the GBP has changed the meaning of the overnight benchmark (April 2018) but has kept its name unchanged. The USD has created a new benchmark (SOFR, April 2018) and has kept the existing one (EFFR). The EUR has created new benchmark (ESTR, October 2019) and has at the same time changed the meaning of the old one (EONIA) and in a second time (January 2022) stopped the publication of the old one.

On the IBOR side, in GBP the LIBOR is declared non-representative from January 2022, will continue to exists to December 2022 in a synthetic form and its status for after January 2023 is still unknown. In USD, LIBOR is declared representative to June 2023, but new LIBOR trades should stop from January 2022; its publication will probably stop after June 2023. In EUR, EURIBOR will continue and there is not planned publication discontinuation.

On the volume side (as measured by interest rate derivatives cleared at LCH), if we consider only the above 3 currencies, the overall volume YTD for 2021 (IRS, OIS, basis, FRA, etc.) is split 52.5% for USD, 26.0% for EUR and 20.6% for GBP.

Looking only at the trades indexed on the new overnights (SOFR, ESTR, SONIA), one would expect a split where the EUR portion is inferior - EURIBOR continues - and a relative split between GBP and USD - both LIBORs should not be traded as of next week. What we see is very different. Taking only into account the last 8 weeks with published data at LCH, we have 24.0% for USD, 27.9% for EUR and 48.1% for GBP. The weekly comparison is provided in Figure 1. Even when compared with EUR, for which there is less overall volume and for which the IBOR will not stop, the SOFR volume is inferior. We are still far away from SOFR first. We will see what 2022 bring on that front.

Figure 1: Weekly volume for ESTR, SOFR, and SONIA linked derivatives at LCH (in USD billions equivalent).

Unfortunately, the volume for OTC trades on the other USD Credit Sensitive Rate BSBY are not available. For the futures, some figures were provided in a previous blog; USD SOFR First in numbers - 22 Dec 2021.

Saturday 25 December 2021

Cash settled swaption pricing with Swap Rate Fallback - working paper

Swap Rate: cash settled swaptions in the fallback


With the planned cessation of LIBOR, the LIBOR-based Swap Rates will also cease. For legacy transactions linked to it, a fallback is required. Some approximated fallback mechanisms have been proposed by working groups. The approximations involve some non-linear function of overnight-based swap rates. Due to the non-linearity, cash settled vanilla swaptions are becoming exotic products. Moreover, keeping the annuity unchanged while changing the rate to overnight-based swap generates technical issues in the pricing leading to convexity adjustments. The article proposes different pricing methodologies for those now exotic swaptions, including several price approximation to reduce the implementation numerical complexity.

Different working groups have proposed fallbacks for the Swap Rates indirectly based on the mechanism used for LIBOR itself. This is the case of the Sterling working group in Working Group on Sterling Risk-Free Reference Rates and the USD working group in ARRC (2021). Those fallbacks are based on OIS versions of the Swap Rates. IBA is publishing GBP SONIA ICE Swap Rate since 14 December 2020 and USD SOFR Swap rate since 8 November 2021. Refinitiv is publishing the Tona Tokyo Swap Rate since 28 October 2021.

For reasons summarised below, it is not possible to create a Swap Rate's fallback coherent with the LIBOR's fallback. Or more precisely it is possible (and easy) for a quant to do so, based on the swap market globally, but it is impossible for a lawyer in a definition involving a single number. The self-imposed restriction on the fallback type available make the existence of a coherent fallback impossible. In the absence of an exactly coherent fallback, the above mentioned working groups' documents tried to provide formulas for an approximatively coherent one.

In this paper we do not discuss the quality of the approximation — some discussions are available in one of Marc's blogs — but the impact of the type of fallback selected on a liquid vanilla market instrument: cash settled swaptions with collateral discounting.

The proposed replacement for GBP LIBOR ISR by the Working Group on Sterling Risk-Free Reference Rates (2021) is displayed in Figure 1. Formulas with similar mechanisms have been proposed for USD and JPY.

Figure 1. Approximated formula proposed by the WGSRFRR for ICE Swap Rate fallback.

After fallback, a cash settled swaptions with collateral discounting payoff becomes

The non-linear pay-off part of the problem will be decomposed in two issues: strike and exotic feature. As the rate is transformed by a non-linear function, finding at which OIS rate the former IRS swaption will be exercised requires a little bit of work: inverting the function f. Once the strike is known, there is the question of the payoff, which is given by the same non-linear function. It is not a vanilla swaption anymore; a simple strike's shift or multiplier is not enough. In our pricing approach we provide approximations that estimate the impacts of the different parts.

The swaption value is usually obtained by expectation in the IRS physical annuity associated measure. The two issues are the ``wrong'' annuity and the non-linearity f.

We first change the measure to the OIS physical annuity associated measure. Then we approximate the ratio of annuities by a function h of the OIS rate:

Using standard replication argument, the price can then be written as

The paper also proposes several approximation to the price by full replication. The approximations are based on simple change of strike, order 1 approximation and order 2- approximation. The approximation can be used for themselves in case of short term options. We use them mainly to clarify which issues have a significant impact on the price.

The replication formulas and all the approximations have been implemented in our production grade library.

Preliminary versions of the results were presented at The 4th Interest Rate Reform Conference (20-21 October 2021) and at The 17th Quantitative Finance Conference (17-19 November 2021). 

The full paper has been submitted for publication in November.

Don't hesitate to contact us if you want to implement such approach or validate your own implementation.

Happy New Year

Wednesday 22 December 2021

USD SOFR First in numbers

Over the last 5 months, several "SOFR First" dates have been initiated by US regulators. With the January 2022 date approaching, this post review were we stand on this issue for the two main source of liquidity in the interest rate market: swaps and futures.

The post is based on public data from LCH, ISDA and CME for futures.

On the swap side, the SOFR portion in volumes continue to increase. The volume is now above 1,000 billion a week every week. But the increase is not spectacular. From the ISDA figures, it appears that a couple of weeks before the theoretical deadline, we are roughly at LIBOR 75% - SOFR 25%.

Figure 1: SOFR - LCH volumes and ISDA reported volumes

On the futures side, the transition is even less spectacular as reported in Figure 2. There the situation is (over the last month) LIBOR 83% - SOFR 10% - Fed Fund 7%.

Figure 2: LIBOR and overnight futures at CME. Daily volume (in thousands).

From our perspective, it is difficult to understand where this is coming from as by trading futures with maturity beyond June 2023, one effectively trade a SOFR futures under a different name. A financial reason that may warrant such trade is the expectation that the transition will not take place and hope for a larger/smaller spread that the one implied by the CME announced conversion mechanism. But such an explanation for a so large volume does not appear realistic. Maybe a more down to hearth explanation is that the market is not ready from a system, back office, validation or limit prespective. The users trade LIBOR futures, even if they are convinced that they are SOFR futures under another name, because they are not allowed to trade SOFR futures directly.

The slow transition of the eurodollar futures as been also reported in the press. See "SOFR First" for Eurodollars downgraded to "best practice".

Even for overnight futures, the SOFR futures are not the only player as reported in Figure 3. The Fed Fund futures still trade in a large volume. On the one-month futures side, the Fed Fund futures volume is well above the SOFR futures.

Figure 3: Overnight futures at CME. Daily volume (in thousands).

The futures graphs also provide some figures for the BSBY futures. The volume is present, but an order of magnitude or two below the SOFR futures (0.1% of total futures volume in the last month). This reinforce our opinion that the continued trading of LIBOR futures is a sign of lack of market readiness in the transition. Trading of LIBOR futures is not trading bank funding, that would be better done through BSBY futures; trading of LIBOR futures is not trading monetary policy, that would be better done through SOFR futures. What appear to be traded in LIBOR futures is the "inertia" of the market, the difficulty inherent in changing or discontinuing something that has been at the core of the interest rate market since the 80's.

Saturday 11 December 2021

USD benchmarks and spreads

With a couple of weeks left to the LIBOR big crunch, we review the market situation in term of "spreads".

There has been a push to not only correct the LIBOR weakness but also from certain quarter to try to kill the idea of credit sensitive benchmarks. With many trillions of financial instruments referring to credit sensitive benchmarks and LIBOR in particular, the impact of removing the credit sensitivity is, on a gross basis, many trillions multiplied by many basis points, i.e. a huge amount. That huge amount is the so-called value transfer in the transition.

In this blog we don't try to estimate the "many trillions" part, but to review with actual market data the order of magnitude of the "many basis points" part.

The USD market is both the largest financial market and the one where more benchmarks related to those issues are publicly available, so we focus on that market.

Some of the available benchmarks are:

  • SOFR: Secured Overnight Financing Rate, a secured overnight rate published by the New York Federal Reserve.
  • LIBOR: London InterBank Offered Rate, and unsecured term rate published by IBA. Its CHF, GBP, and JPY version will stop publication on 2021-12-31. Its USD version will stop publication on 2023-06-30, but to some extend its use for new trades will be forbidden as soon as 2022-01-01.
  • AMERIBOR: There are several version of it, and here we focus on the 30-day term rate with ticker AMBOR30T
  • Bloomberg BSBY: Credit sensitive term benchmark based on actual bank funding transactions.
  • IBA BYI: Bank Yield Index. To some extend similar to BSBY but only in beta version at the moment.

LIBOR rates have been accused to be manipulated, probably with reason in the first 10 years of the millennium. If manipulation was the problem, one could simply have reformed them instead of discontinuing them. Are LIBOR rates still manipulated? Figure 1, tends to lead to a "no" answer. It displays LIBOR and different other indices, most of them IOSCO principles and BMR compliant, that promise to represent the same bank cost of funding. Through the recent Wuhan born pandemic and Fed provided liquidity flooding, the appearance is the same: the different indices are at very similar levels and move in sync. No sign of major manipulation is visible.

Figure 1: Historical data for different spreads.

To deal with the forced LIBOR disappearance, an artificial fallback mechanism has been created. It relies on a fixed spread between some measure of SOFR on the LIBOR tenor and LIBOR itself. That spread is fixed and unique for each LIBOR index. What has been the behaviour of the actual spread in the market over the last years? All time series represent the spread between the above mentioned indices and term SOFR. The ISDA proposed spread, copied by CCPs, regulators, and lawmaker is displayed in red. Both in case of crisis and the recent data, this fixed spread has been far away from a bank funding level fair representation.

In Figure 2, we focus on the last 6 months. The proposed spread has clearly been 10 to 15 basis points too high. Actual lending have reflected this reality, with spread to SOFR well below LIBOR spread if the artificial spread is used as a reference.

Figure 2: Historical data for different spreads, last 6 months.

The spread has been computed as the 5-year median between LIBOR in advance and SOFR in arrears. So it includes the credit/liquidity term spread but also the in-arrears/in-advance spread, i.e. the misestimation by the market of the short term (next 3 months) monetary policy. The impact of that misestimation is displayed in Figure 3. The pandemic induced rate cut has created a significant (up to 120 bps) misestimation; that misestimation is embedded in the computed spread.

Figure 3: Historical data for the spread between ISDA SOFR 3-month methodology and ARRC recommended SOFR 3-month term rate.

Is this analysis relevant or just a theoretical computation without practical impact? This spread is used for 100 trillions of financial products. From a risk management point of view, the important figure is Figure 1. The change of benchmark impairs the risk management features by as much as 100 basis point, certainly a non-negligible level. For some this may be an improvement, but certainly it is not an impact-less transition. From a valuation perspective, the important point is the expected value of the changes. The spread as been computed as median — not a mean —, so there is no a priori relation between the figure used and the actual valuation impact, even if the spread figure was computed properly. In practice the difference is, for USD-LIBOR-3M, a median of 26.161bps ("official" figure) and a mean of 32.583 bps. That is more than 6 bps between the two. If the "technical" choice done by ISDA and its member had been "mean", you would be richer (or poorer) by 6 bps on all your USD-LIBOR-3M payments for the rest of times!

In between the "wrong" rate (in-advance/in-arrears) and the wrong statistical measure (mean/median) there is a lot that can go "wrong" from a value transfer perspective. Looking at the issue from different perspectives, you can certainly find different answers. But in all cases, a realistic order of magnitude is around 10 basis points.

All those issues do not stop on 1 January 2022. The impacted trades may stay in the books for many years or may have been amended in an unfair way. Some items to keep in mind:

  • the management of the fallback process is extremely complex, even with a fixed spread (see here),
  • the spread fixing mechanism/protocol may have been done incorrectly and you need to claim some compensation (see here)
  • the impact on non-linear products is more complex than a simple spread change (see here)
  • EU regulation forces the use of "in-advance" fixing for CHF LIBOR, with potentially significant convexity adjustment impacts
  • CCP transition is not equivalent to bilateral transition, back-to-back trade may not be back-to-back anymore

This is only a small list of potential issues. Don't hesitate to contact us for advice on those and related issues. Better safe than sorry; a couple of days worth of advice can save you years and millions in litigations or financial losses.

Wednesday 10 November 2021

Volume in overnight-indexed derivatives


With the disappearance of EONIA (at least in the cleared world), ESTR continues in line with previous weeks.


SOFR also continues to progress. But still below 15% of the IR derivatives (as reported by ISDA Swap Info) and far away from SOFR first.

On Monday (2021-11-08), IBA launched the USD SOFR ICE Swap Rate.


CHF-LIBOR is disappearing in roughly 6 weeks. SARON, its only competitor, continues to progress slowly. We would not say it is a complete victory yet.

USD futures

On the Exchange Trade (Futures) side, LIBOR is still the USD leader, by a wide margin.

If we zoom in on the alternatives, we see a host of other contract types. Beyond SOFR, there is EFFR, BSBY and AMERIBOR. The good old Fed Fund futures (1 month, arithmetic average) is still the most traded contract after LIBOR on some days. The volumes for BSBY and AMERIBOR are significantly smaller by not completely negligible. They also help to assess the value transfer embedded in the LIBOR fallback.

LIBOR contract beyond July 2023 will be converted in SOFR-3M futures in June 2023. Still more liquidity in the LIBOR futures than in SOR futures even after July 2023. Why? Two hypothesis: one not good for the state to the financial industry and one not good for the state of the transition.

Hypothesis 1: Financial institution not ready for SOFR futures. This can be due to valuation and risk (SOFR futures have a different convexity adjustment and a different apy-off) or operational (settlement is at the end of the period, based on compounded rate) issues. Trader would use LIBOR futures because their institution cannot cope with SOFR futures, even if they know that they are not really trading LIBOR futures. They hope than in the next 18 months their institution will be ready, but clearly they are not ready yet.

Hypothesis 2: Trader have a very good understanding of the issue but believe that there is still a chance that USD-LIBOR will not stop at end of June 2023. The LIBOR futures are trading at the ISDA/Bloomberg spread to SOFR futures. They can be seen as a free option on the non-cessation. If everything goes as planned by regulators/IBA, no loss; if cessation is postponed, a big profit (if the position is in the right direction). But that would be a one sided bet, who is taking the opposite direction? People certain of the transition? People not aware of uncertainty in the transition? People not aware of the transition?

I don't know which of the two is true or if a third hypothesis should be incorporated.

SOFR is certainly taking some volume from USD-LIBOR. But BSBY is also coming to life. A little bit of volume on the futures side (7,500 ADV or so) and commitment by the two main USD Swap clearing houses (CME and LCH) to start clearing BSBY IRS by year end. The USD Game of Benchmark is on, now more than ever.

Tuesday 26 October 2021

SOFR and ESTR: a real boom?

Over the last months, our analysis in relation to ESTR and SOFR has been something like "small improvements".

This week the summary could be: a real boom!

The situation is very different in USD-SOFR and in EUR-ESTR, even if the result are similar.


Let's start with the EUR-ESTR. EONIA has been the main overnight benchmark up to recently even if EONIA is derived from ESTR as ESTR+8.5 bps since October 2019. In two years, the real underlying had not been able to overtake the old and broken incumbent. EONIA will stopped to be published as of 1 January 2022.

On 15 October, the CCPs have cancelled the existing EONIA swaps and replaced them by ESTR swaps. No more EONIA swaps at CCPs but many ESTR swaps. This is clearly visible in the graph below (LCH volumes).

Note that at almost the same time (on 21 October), the EU published a text of law mandating the replacement of EONIA by ESTR + 8.5 bps. When it was announced that EONIA data collection would be stopped (somewhere in 2018) and replaced by ESTR + spread, Marc said that he believed that the synthetic EONIA would last for very long. He was quickly proven wrong with the announcement that EONIA publication would be stopped on 1 January 2022.

Now he is proven right again by the law! Three years were no enough to deal with this transition. This is in line with another (even older) prediction: Change of benchmark overnight index is a difficult task. Another prediction was that EONIA would stay for a very long time in bank systems as a fixing and as a curve. Note that the EONIA replacement by ESTR+8.5bps is only for contracts for which the EU law applies.


For SOFR, there was no specific news, but a real progress in term of volume nevertheless.

A significant increase in absolute volume both at LCH and in the ISDA figures (US regulatory figures). The relative volume is still below the 15% of the total LIBOR + SOFR. The USD market is still far away from SOFR first!

Wednesday 13 October 2021

ICE Swap Rate fallback: impact on swaption pricing

Sterling and dollar working groups have proposed fallback for ICE Swap Rates (ISR) based on the mechanism used for LIBOR itself. It is not possible to create a ISR's fallback coherent with the LIBOR's fallback. Or more precisely it is possible (and easy) for a quant to do so, based on the swap market globally, but it is impossible for a lawyer in a definition involving only one number published on a single screen.

The self-imposed restriction on the type of fallback available make the existence of a coherent fallback impossible. In the absence of an exactly coherent fallback, the working groups tried to provide an approximately coherent one.

The impacts of those fallback go beyond simply printing a formula on a piece of paper and have profound impacts on the valuation and risk management of existing instruments like swaptions.

In particular cash settled swaptions with collateral discounting have a triple problem:

  • Incoherent spread (delta hedge with swaps)
  • Non linear pay-off
  • ``Non-natural'' annuity, i.e. convexity adjustment

The incoherent spread was discussed by Marc in a previous blog: LIBOR transition: How to lose money, automatically!

In a forthcoming paper, we will show how those swaptions can be priced.

The one line summary of the pricing method is a change of strike in line with the non-linear rate transformation and a replication similar to the one used in CMS pricing.

Some early results have been presented in LIBOR transition workshops. A more detailed seminar related to the swaption pricing will be presented at The WBS 17th Quantitative Finance Conference.

Below we already proposed a graph that displays the non-linearity impact, the exact meaning of which will be discussed in the seminar. We will post a link to the full paper once published.

Note added 20 October 2021: A preliminary version of the results were presented at The 4th Interest Rate Reform Conference today.

Note added 20 October 2021: I have added the ICE Swap Rate fallback formulas to my open source library muRisQ-ir-models at

SOFR volume to 8 October 2021

Usual review of SOFR volumes. After a small increase a couple of weeks ago that lead us to ask "Is something happening?", we are back to levels below mid-July level at LCH. ISDA figures indicate that SOFR is back to less than 10% of interest rate derivatives volume.

No real progress a little bit more than two months before the expected deadline for "no more LIBOR".

Short term swaps (less than 2Y) volume is not increasing either, which is not a good indication for the development of Term SOFR rates.

Tuesday 28 September 2021

SOFR: Is something happening?

Weekly volumes of interest rate trades. Is SOFR slowly waking-up? Weekly volume last week are the highest ever, higher than mid-July. ISDA reported figures (US only) have the highest percentage of SOFR outright volume (almost 14%).

The ISDA data (representing data reported to US regulators) is growing faster than the LCH data (international markets). Does it means that international users are slower to move to SOFR and that we could have two markets: a local market (with local regulatory pressure) and an international market (with more market freedom)?

Note that we have change the definition of relative portion in the graph. The outright SOFR is now reported as portion of all trades, not portion of LIBOR trades. This is to avoid "infinite" results when LIBOR will disappear. The portion is now capped at 100%.

Tuesday 21 September 2021

SOFR first - two months on

Presented without comments this week.

Comments on ESTR, SARON, and SOFR to come later!

Tuesday 14 September 2021

Decrease in SOFR activity

We are not certain of its origin, but certainly a significant decrease in SOFR activity last week. The lowest in the "SOFR First" era at LCH and lowest in 5 weeks for the ISDA reported figures. But the ISDA reported figures indicated a relative increase with respect to LIBOR.

It is not clear what the origin of this is. One potential explanation is market moving out of LIBOR but not to SOFR.

CME futures on BSBY provide a view of market price discovery of SOFR v credit sensitive rates. For those that have not yet agreed on the fallback for legacy LIBOR trades, that opens a window on valuation impacts.

This makes Marc's cautionary tale published in January 2020 edition of Risk even more tangible. It is now possible, to some extend, to measure the exercise value of the protocol option. Marc mentioned the "Fallback protocol as an option" in the past, in particular in the blog "ISDA Fallback as an option".

For the (low volume for BSBY and SOFR) trades on the September 2023 contract (first after USD-LIBOR cessation), the spread LIBOR-SOFR is 27 bps and the spread BSBY-SOFR is 19 bps. The first one is roughly in line with the CME Eurodollar futures fallback using ISDA/Bloomberg spread (26.161 bps), the second one provides the cost of protocol signature for a September 2023 fixing: losing or making 8 bps. Lets wait for more volume on the longer term part to assess more of the value transfer. We will try to provide more data on BSBY in a forthcoming blog.

Wednesday 8 September 2021

SOFR first - six weeks on

No big push since "SOFR First" date six weeks ago. Quite flat volume, both on the weekly figures and on the monthly figures. Using ISDA figures, SOFR outright OIS volumes still less than 10% of LIBOR volumes.

Workshops with CQF insitute

Marc Henrard will present two workshop with the CQF insiture.

The first one will take place on Wednesday 6 and Thursday 7 October 2021.

The second one will take place on Tuesday 9 and Wednesday 10 November 2021.

The agendas of the workshops can be found on the webpages references above.

Don't hesitate to contact us if you want to organise similar workshops in-house.

Tuesday 31 August 2021

SOFR first - five weeks on

No big push since "SOFR First" date five weeks ago. Using ISDA figures, SOFR outright OIS volumes still less than 10% of LIBOR volumes.

Wednesday 25 August 2021

SGD SORA figures

On popular demand, we also publish some SGD SORA figures. 

Figure 1. Monthly figures (to July 2021) for SORA clearing at LCH.

Figure 2. Weekly figures (to 20 August 2021) for SORA clearing at LCH.

Tuesday 24 August 2021

Workshop at the 4th Interest Rate Reform Conference - 19 October 2021


Marc Henrard will present a workshop at

The 4th Interest Rate Reform (Ibor Transition) Conference

which will take place on-line from Tuesday 19 to Thursday 21 October 2021. The agenda of the conference can be found on the organizer web site:

Marc's workshop will take place on Tuesday 19 October from 13:00 to 17:00 and will be titled  

LIBOR transition: almost there and so much to do for quants.


  • Liquidity in ESTR, SONIA and SOFR
  • Multiple fallbacks, multiple market risks, one spread to rule them all!
  • ISDA fallback spreads v recent LIBOR/SOFR data
  • USD: alternatives to SOFR - AMERIBOR, BSBY, ICE BYI, AXI, CMT
  • Hidden issues

ESTR and SARON: weekly figures

Weekly figures for ESTR and SARON at LCH.

In both cases, no real progress over the summer.

Monday 23 August 2021

SOFR first - four weeks on

Looking at last week SOFR numbers, the only description that comes to mind is "unchanged to slightly lower". No big push since "SOFR First" date four weeks ago.

LCH figures slightly lower, ISDA figures slightly lower, ISDA outright SOFR as portion of LIBOR slightly lower.

Sunday 22 August 2021

USD transition - quick spreads review

We still have roughly four months to go to the LIBOR transition. USD-LIBOR rates will still be published for 18 months after that, but the goal is to stop adding more LIBOR exposure from the beginning of 2022 onward.

A fallback mechanism for legacy LIBOR has been proposed by ISDA, based on a historical spread approach between the in-advance credit risky LIBOR and the in-arrears secured SOFR. The results of that historical spread computation has been announced on 5 March 2021. FOR USD-LIBOR-3M, the result was a spread of 26.161 basis points.

In USD, other mechanisms to replace LIBOR have been proposed. They include, among others (see this blog for more alternatives) Bloomberg BSBY, CME SOFR Term rates, and AMERIBOR. In this blog we propose recent historical data related to those benchmarks.

The data themselves are IBA USD-LIBOR-3M (2019-01-02 to 2021-08-20), Bloomberg BSBY 3M (2019-01-02 to 2021-08-20), SOFR Term rate 3M (2019-01-03 to 2021-08-19), SOFR compounded using ISDA mechanism (computed from Fed raw data) (2019-01-02 to 2021-05-17), and AMERIBOR 90D (2021-05-17 to 2021-08-20). The SOFR compounded time series are shorter by 3 months due to the in-arrears feature. The AMERIBOR 90D is published only since May this year. The time series are displayed in Figure 1.

Figure 1: Historical rates from beginning of 2019 to today

The drop of rates after COVID-19 pandemic spreads from Wuhan to contaminate the world is clearly visible in the graph at the beginning of 2020. The way the different rates reacted was different.

In Figure 2, we display the spread between LIBOR and the other rates. The BSBY spread has also jumped around that time, but remained contained. The Term SOFR had one big jump that can be interpreted as a market credit concern. At the opposite, the compounded in-arrears ISDA style had two large jumps, probably one due to the delayed nature of in-arrears and one related to credit.

Figure 2: Historical spreads to LIBOR from beginning of 2019 to today.

For the period in the graph, the statistics for the spreads are an average of 5 bps and a standard deviation of 4.6 bps for BSBY. For SOFR Term, the statistics are an average of 23 bps and a standard deviation of 21 bps. For SOFR in-arrears with ISDA methodology, the statistics are an average of 32 bps and a standard deviation of 30 bps. For AMERIBOR 90D, the statistics are an average of -1.7 bps and a standard deviation of 1 bps; the period of reference is very different and those statistics cannot be compared to the previous ones that are reported on a substantially more unstable period.

The fallback method is based on a fixed spread of 26.161 bps (and an implicit standard deviation of 0).

Added 2021-08-28: The spread versus term SOFR is presented in Figure 3. LIBOR, BSBY and Ameribor spreads varied widely but are all positive, except one date for LIBOR (2 March 2020). Over the last year, the spreads have been well below the ISDA spread fixing.

Figure 3: Historical spreads to term SOFR from beginning of 2019 to today.

Wednesday 18 August 2021

SOFR first - three weeks on

SOFR First started on 26 July. We now have three weeks of data. The results are still somehow mixed.

On the LCH front, the volume is again significantly below the 30 July week level (SOFR First initial week).  The volume is roughly the same as at the end of May.

On the ISDA figures side (from US regulatory figures), the absolute volume is up for the 6th week in a row; the volume has tripled in those weeks. But the figures reported by ISDA (USD 166 bn) are well below the figures reported by LCH (USD 520 bn). 

A temptative interpretation could be that the US local market is moving slowly to SOFR (SOFR volume is now around 11% of LIBOR volume). Even if that move represents a real chance in behavior, it impacts only a small portion of the USD market. The figures published indicate that ISDA actually captures less than a third of the SOFR market in its SwapInfo analysis.

Note: More volume analysis over the last years available on Marc's multi-curve framework blog.

Tuesday 10 August 2021

SOFR first - two weeks on

SOFR First started on 26 July. We now have two weeks of data. The result is somehow mixed.

On the LCH front, the volume has decrease significantly last week with respect to the previous one (SOFR First initial week).  The volume is roughly the same as in end of May.

On the ISDA figure side (from US regulatory figures), the absolute volume is slightly up but the proportion of SOFR with respect to LIBOR is down; it is below 8%.

Still far away from SOFR First!

Note: Blog initially published at: More volume analysis over the last years available on Marc's multi-curve framework blog.

Sunday 11 April 2021

New publication: Derivative pricing with two collateral rates

A new working paper related to convexity adjustment in the overnight ransition has been made available on SSRN. The paper title is

Derivative pricing with two collateral rates.

The paper is available on SSRN at


This note analyses derivative pricing in the context of a collateral rate switch during the life of a financial product or the existence of two overnight rates. In particular we analyse the impact of forward change of collateral, the impact on OISs when the collateral rate is different from the OIS underlying, and the impact of bilateral swaptions collateral rate different from the one implied by the cleared market. In each case, we evidence new convexity adjustment impacts previously not accounted for. The order of magnitude of those impacts is also proposed for realistic values of model parameters; the individual relative impacts are not huge, but when applied on trillions of notional, as it is the case, the monetary impacts can be substantial.

Sunday 28 February 2021

Marc quoted in the press: Practice Insight - IFLR

Marc was quoted in the press in an article related to the LCH steering away from ISDA fallback: Industry broadly supports LIBOR big bang switch (subscription required).

The quotes are

While the proposal crafted by LCH may look like an ideal solution for many market participants, it could come at a price, which some deem too high. “I encouraged my clients to consider this approach even before it was proposed by LCH, but we should bear in mind that clearinghouses look at what is in their books – not at the market,” said Marc Henrard, managing partner at muRisQ Advisory.. “They want to push the bifurcation problem out to end-users, who in turn will have to deal with the issue on their bilateral trades and manage the bilateral-to-cleared basis risk."

Bringing forward this proposal earlier and presenting a common mechanism that can also apply to bilateral trades would have made for a smoother process, Henrard added.
In addition, there is a risk that LCH's solution could fragment the swaps market, as liquidity will be split between the trades referencing RFRs and those using ISDA’s fallback rates. “Market participants should make sure they have the right tools in place to compute any small residual valuation difference,” said Henrard. “LCH’s proposal may not work out to everyone’s advantage, and some may want to adjust their positions ahead of the big bang.”

Thursday 25 February 2021

CQF Institute Workshop: Benchmarks in Transition

Marc Henrard will present a two half-day workshop

Benchmarks in Transition (LIBOR and Overnight)

organized by the CQF Institute on 18 May 2021 and 19 May 2021 (on-line 13:00 - 17:00 BST).

The agenda of the workshop can be found on the organizer website:

The agenda of the workshop will be similar to the one proposed on our training page.

The workshop is also availabe as a in-house course for financial institutions. If you want to be ahead in the transition game, contact us for LIBOR fallback and discontinuation: trainings, workshops, advisory, tools, developments, solutions.

Wednesday 17 February 2021

Presentation at the Interest Rate Reform Conference

Marc Henrard will present a seminar at

The 3rd Interest Rate Reform (Ibor Transition) Conference

which will take place on-line from Monday 22 February to Friday 26 February 2021. The agenda of the conference can be found on the organizer web site:

Marc's talk will take place on Wednesday 24 November at 13:00 GMT and will be titled Benchmarks in transition: Hidden convexities.


  • Overnight transition: why is it important to everybody?
  • Overnight transition: where does it appear?
  • Modelling approach
  • Impact on OIS
  • Impact on Swaptions
  • Impact on LIBOR forwards

The proprietary research underlying the presentation will be detailed in a forthcoming working paper. The link to the paper will be added soon.

Tuesday 19 January 2021

Inconsistencies in fallback spread for different tenors

With the recent consultations on different dates for USD-LIBOR and other currencies LIBOR cessation, the discrepancy in spread computation mechanism has been discussed.

To our opinion, there will be no date discrepancy as we expect the LIBOR cessation announcement date to be the same for all currencies, even if the cessation date is not the same.

There are other more important inconsistencies. In the cross-currency market, there is the obvious LIBOR v (IBOR but not LIBOR). EUR-EURIBOR will not cease and the major cross, the one between USD and EUR, will be the prime example of this inconsistency.

But the other, less talk about, inconsistency that we want to point out in this post is the tenor inconsistency within a single currency. The spread for all tenors will be computed on the same day using a look-back period of 5 years. The period for all currencies is nominally the same 5 years, but those 5 years represent different economical realities for each tenor. The differences are coming from the fundamental flaw in the fallback spread methodology which is comparing a forward looking rate to a backward looking composition. To compare those two rates, you have by definition to use different dates. For LIBOR there is one fixing date while for the overnight, there is a tenor-full of dates.

Take the example of the USD-LIBOR-12M. Suppose that the announcement date is on 2021-01-05. What is the meaning of 5 years? This is the most recent 5 years of LIBOR fixing for which we have the corresponding 5 year of SOFR composition over the LIBOR tenor. The period starts on 2015-01-05 and finishes on 2020-01-05. The end is in 2020 and not 2021, even if the announcement is in 2021. This is not a typo but the impact of the in-arrears. To compute the spread, we need the in-arrears compounded on a 12 months period, i.e. the period from 2020-01-05 to 2021-01-05. This is a little bit more complex than that, because of the -2 business day shift in the fallback, but for this post we ignore it (all our data analysis and graphs are produced with the exact rules implemented in a production grade library).

But if we look at the same question for USD-LIBOR-1M, the LIBOR period is 2015-12-05 to 2020-12-05, a 11 month difference with USD-LIBOR-12M, i.e. almost 20% of the period is different. This is very significant when the economical situation is not stable. It turns out that the last 12 months have been very unstable from an economical perspective.

Let's look at it through the lens of the spread data. In Figure 1, we have represented the spread computed on a daily basis of the LIBOR/SOFR compounded in-arrears for tenors 1M, 3M, 6M, and 12M using the ISDA methodology.

Figure 1. Historical spread between USD-LIBOR and SOFR-compounded for different tenors.

Contrary to the intuition of the spread as being a credit spread, we see that the curves cross in several places. The 12M spread can be in some periods below the 6M and even the 3M spread. The April credit spread increase is clearly visible in the 1M, 3M and 6M spreads. Is it visible in the 12M curve? The answer is definitively no. The USD-LIBOR-12M data for the March/April period is not used, only the LIBOR data to 2020-01-05 is used. What is the spike seen at the end of the curve? This is the market misestimation of the monetary policy. SOFR, which closely follow monetary policy, over the last year crisis is strongly impacting the spread, but not for credit risk reason. The spread there is the "wrong" one if the goal is to represent the credit spread, it only represents the market inability to predict the future rates. Is what we want to represent in the spread? Usually a floating rate instrument is there to avoid the future's prediction. In this case, the spread represent the opposite of what we would like. A second spike will appear in the next 3 months and represent the credit spread effect.

This discrepancy can also be viewed in Figure 2.

Figure 2. Distribution of spread for USD-LIBOR-12M. 

We have represented the distribution of the spread with the most recent data in a lighter colour. The recent spreads are high while today all the rates are low, the forward spreads are low due to the injection of liquidity by central banks and all short term historical spreads are low. The same economical reality produces completely opposite effects on different figures that are supposed to provide a fallback to the same LIBOR reality.

Recent related post: Historical spread adjustments: GBP figures, Historical spread adjustments: USD figures and CME steers away from ISDA fallback.

Fallback transformer series: LIBOR Fallback transformers!

LIBOR transition page.

Don't fallback, step forward!

If you want to be ahead in the transition game, contact us for LIBOR fallback and discontinuation: trainings, workshops, advisory, tools, developments, solutions.

Sunday 17 January 2021

Historical spread adjustments: GBP figures

We compute estimates of the historical spread adjustment for GBP-LIBOR on a regular basis. The data below is as of 2021-01-04.

Current Median 3.4773 12.2818 27.8621
Minimum Median 3.4305 11.4454 25.2390
Maximum Median 3.5505 12.4071 28.9121
Mean 3.6657 13.8936 27.095
Mean-Median 0.1884 1.6118 -0.7671

Contact us for more details on the hypothesis and methodology used.

We can provide production grade code that run those estimates on a daily basis.

Figure: Distribution of GBP-LIBOR-1M / GBP-SONIA compounded in arrears over 1M.

Thursday 14 January 2021

CME steers away from ISDA fallback

Since the discussion related to the fallback have started almost three years ago, our opinion has been that the methodology proposed, in particular by ISDA, based on compounded in arrears are unsatisfactory. The compounded in arrears itself is the correct approach for overnight, but forcing an overnight in-arrears mechanism into instruments designed for term in advance rates can only lead to dangerous situations from a risk management perspective.

Marc has been quite vocal about it in his blogs and technical publications. The earlier warning can be found in his quant perspectives (proposal, July 2018 and results, January 2019) and blogs (e.g Fallback compounding in arrears won't work).

Recent presentation to clients included in particular messages like:

Don't sign the protocol, don't go through the fallback, this is a unmanageable Frankenstein.

Our advise, in the same presentation was

Fallback does not create OIS-like exposures. Better to repaper existing LIBOR swaps to OIS (even if with same spread).
muRisQ Advisory presentation to a client on 17 December 2020.

There was a general believe that CCP would adopt the ISDA protocol. But in the same client discussion we said: "CCPs do whatever is the easiest for them, not what is right for the market. We still have to read the details of the CCP fallback"!

CCPs have full discretion on how to incorporate fallback.
muRisQ Advisory presentation to a client on 17 December 2020.

We invite you to (re)read of previous blog related to the reason why the proposed ISDA fallback is not acceptable in term of risk management: Fallback transformers: gaps and overlaps and its portfolio or Christmas versions.

LCH recently indicated that it does not plan to use the fallback, as described in the press and in the blog: LCH plans Libor swap switch to RFRs

CME appears to also follow our lead and suggest not to use the fallback. Today's announcement "Cleared Swaps Considerations for IBOR Fallbacks and Conversion Proposal" offers a very short overview of the conversion direction.

The discussion document ask about timing, calculation periods, coupon payment dates, and swaption exercise. Those issues have been mainly ignored in previous consultations and in the collateral/discounting big bang.

We have provided in detail analysis of all those issues to several clients, buy side and sell side. The analysis are all based on production grade code implementing all the successive versions of the fallback, including all the timing, dates and spread issues. Hopefully detailed independent analysis of those issues will be performed and made public by the CCPs.

Don't fallback, step forward!

If you want to be ahead of the transition game, contact us for LIBOR fallback and discontinuation: trainings, workshops, advisory, tools, developments, solutions.