muRisQ Advisory offers quantitative finance advisory services. Its services focus on trainings and workshops, benchmark transitions, interest rate model development and validation, product design and risk management strategies.
Marc will present at the Quant Insights Annual Conference on 1 November 2023 (free online tickets available).
Marc's presentation will be based on his recent paper
Don't hesitate to contact us if you you are interested by implemented this approach or other term structure modelling.
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!
We are pleased to announce a new working paper titled
is available in our muRisQ Advisory Model Development series of research papers. The paper is available on SSRN preprint repository at http://ssrn.com/abstract=4542275.
Bond futures are characterised by a set of underlying bonds; the short party has the option to deliver at expiry any of those underlying bonds. Consequently, bond futures embed a choice option between bonds with different maturities and coupons. The delivery mechanism also incorporates conversion factors that create an implicit strike. The option is impacted by different maturities and different moneyness for each bond. It is important to take into account the full term structure of volatility with smile. A recent paper Bang and Daboussi (2022) developed such an approach for swap rate based products like CMS. In this paper we extend their approach to cover futures and apply it to the specific case of bond futures. The method allows the analysis of the impact of smile, term structure of volatility and correlations between rates on the delivery option and convexity adjustment values. All of them have an impact on the valuation and risk management of bond futures.
The paper has been submitted for publication in an international peer-reviewed journal.
All the results presented in the paper are based on a proprietary implementation extending a production grade open source quantitative finance library. We would be glad to provide model development or model validation advisory services based on the theoretical and practical development described in the paper. Don't hesitate to contact us if you require advisory services related to the interest rate modelling or benchmark transitions.
LIBOR swaps were converted to SOFR last Friday (2023-05-19 after EOD). The amount outstanding before conversion was around 48 trn, this Friday (2023-05-26) the amount outstanding was down to 15 trn.
Even after conversion, there is still a non-negligible amount outstanding. This is coming from the LIBOR swaps that have still a fixing between the conversion and the last LIBOR representative fixing (2023-06-30). Most of the USD LIBOR swaps are based on USD-LIBOR-3M, with one month to go it is not surprising that around one third of the LIBOR swaps (15 out of 48) still have a representative fixing.
On the OIS side, the notional outstanding increased from 76 to 114 trillions. For OTC products, we don’t see the same offset as in futures that we described in US - Eurodollar futures a USD 8 million rounding error. There is no exact netting as it is same conventions for SOFR vanilla swaps (annual/annual money market) and the converted LIBOR swaps (semi-bond / quarterly money market). Maybe some compression run will reduce the outstanding notional.
The total for IRS plus OIS increased from 124 trn to 129 trn, probably due to the split of former IRS into the LIBOR part and the SOFR part.
Note that over the week, there were still 62 bn IRS and 48 bn FRAs traded. On the IRS side, it is not clear if it is the result of swaption exercise or maybe some BSBY swaps. For the FRA, we don’t have a direct explanation. On the FRA side, not that there is still 376 bn outstanding (unchanged with respect to last week).
We are pleased to announce a new working paper titled
is available in our muRisQ Advisory Model Development series of research papers. The paper is available on SSRN preprint repository at http://ssrn.com/abstract=4461418.
The ISDA designed fallback for cash-settled swaptions with collateral discounting generates swap rate and term structure dependent exotics. To analyse precisely the fallback impact a full term structure of rates and volatility modelling is required. A recent paper Bang and Daboussi (2022) developed such an approach for swap rate based products like CMS. In this paper we apply those techniques to the valuation and risk management of the instruments resulting from the cash-settled and physical delivery swaption fallback. In doing so, we provide some model validation for the approximations previously proposed in this context.
All the results presented in the paper are based on a proprietary implementation extending a production grade open source quantitative finance library. We would be glad to provide model development or model validation advisory services based on the theoretical and practical development described in the paper. Don't hesitate to contact us if you require advisory services related to the interest rate modelling or benchmark transitions.
Last week, Marc presented a workshop on the ”LIBOR transition: What could we have done better from a quantitative perspective?” at the CEETA Benchmark Congress in Warsaw.
Among the elements presented were the results of the fallback on euro-dollar futures at CME that were converted to SOFR futures. An interesting issue with the conversion is the number of decimals. The conversion was done using the ISDA/Bloomberg designed spread between USD-LIBOR-3M and the replacement SOFR of 26.161 bps. This is a number in basis points with three decimals. But the futures are quoted with only 0.5 basis point precision. A natural question is what happen to the extrta decimals? Simply it created a profit for those who understood it.
In the conversion, roughly 4 millions LIBOR futures were converted to SOFR futures, but the open interests in SOFR futures were almost unchanged. The 4 millions futures did not simply disappear, there were offsetting positions between the LIBOR and SOFR futures that had cancelling effects on the next day. The offsets were not between different market participants, but for the same participant having offsetting positions between LIBOR and SOFR futures. The spread between the two was known since 5 March 2021. The amount involved is 4,000,000 contracts with USD 1,000,000 notional each, this means USD 4,000,000,000,000 (4 trillions), not a notional resulting from an ignorant retail trader!
The closing price for the different futures on 14 April 2023 (the conversion date) were:
| Closing prices | Sep 23 | Dec 23 | Mar 24 | |
| ED | 94.965 | 95.33 | 95.785 | |
| SR3 | 95.225 | 95.59 | 96.045 | |
| Spread (bps) | 26 | 26 | 26 |
Take the strategy to buy SR3 at 95.225 and Sell ED at 94.965. The next day, the position is Long SR3 at 95.225 and Short SR3 at 95.22626. The total P/L is, irrespective of the price the next day: (P - 95.225) - (P - 95.22661) = 0.00161%.
The impact of rounding is (number of contracts x notional / basis points / quarterly / offsets * spread)
4,000,000 x 1,000,000 / 10,000 / 4 / 2 * 0.161 ~ 8,000,000
The rounding had an impact of USD 8,000,000.
Given that the spread is known since March 2021, one can guess that market makers have used any opportunity in the last 2 years to add ofsseting positions each time the tradable spread moved away from the 26.161 basis point. The actual arbitrage from the conversion is probbaly well above the figure indicated above.
Hopefully our readers were on the profitable side of the arbitrage.
Don't hesitate to contact us if you require advisory services related to the benchmark transitions.
The implementation note related to the Swap Rates and Term Structure Modelling described in one of our previous post has now been published on SSRN.
The note is available as a muRisQ Advisory Implementation Notes:
The paper is available on SSRN
https://ssrn.com/abstract=4438524.
WThis document contains implementation notes related to Bang and Daboussi (2022). We have extended the original paper by allowing actual accrual factors (not all 1) and non-annual frequency on the fixed side. The note first describes the detailed formulas in this extended setting. In a second part some choices of the implementation and results obtained are provided.
Don't hesitate to contact us if you require advisory services related to interest rate modelling.
Marc will present at the Benchmark Congress organised by CEETA in Warsaw 15-16 May. Most of the congress will be held in Polish and focus on the WIBOR transistion.
Marc's presentation will be divided in two parts
and
Don't hesitate to contact us if you require advisory related to the benchmark transitions.
On Thursday and Friday, Marc was presenting a workshop on “multi-curve and collateral framework and IBOR transition”.
Among the slides presented was this one:
This is a back-of-envelop computation of IM funding cost (Margin Value Adjustment - MLA) to take advantage of the CCP basis. This computation leads to a 1.5 bps annualized at each CCP, i.e. 3.0 bps total. The slide was presented with a graph of the recent LCH-EUREX basis in EUR done a couple of days before and showing the peak at 4 bps for the 10 year.
The same day that the slide was presented, the following article was published in Risk:
This shows that the basis, which looks like an arbitrage, is very difficult to monetize, that 4 bps may not be a strong anomaly but just a feature of the market and that constraints on the market by regulators may have unintended, but not unexpected consequences.
Don't hesitate to contact us if you are interested by independent advise related to market infrastructures, initial margins and interest rate markets.
The USD interest rate derivative market has reached the next "SOFR First"!
We need to qualify that statement. There are many ways to measure what "SOFR First" means. The first "SOFR First" initiative date from July 2021 and consisting of the regulators saying "please use SOFR". Then there were plenty of informal SOFR First
Now it seems we have reached the next "SOFR First" moment (see Figure 1):
Note that we have not reached yet the moment when the outstanding notional on SOFR-linked derivatives at LCH is more than 50% outstanding notional on LIBOR-linked derivatives. We have not reached yet the moment when SOFR is more than 50% of derivative every week. For the moment, EFFR is still above SOFR on a regular basis (see Figure 2).
That moment will come, but it is not clear yet if it will come before the LIBOR transactions are mandatory converted to SOFR.
Figure 1: Outstanding amounts by benchmarks at LCH
Figure 2: Weekly share by product types at LCH
Figure 3: Weekly SOFR volume at LCH and as reported by ISDA (US regulatory figures based).
Marc will be presenting a two-day workshop on the”multi-curve and collateral framework and IBOR transition”. The workshop is organised by CEETA in Warsaw on 23-24 March.
The program is similar to Marc's typical Multi-curve and collateral framework: foundations, evolution and implementation with recent updates on the IBOR transition. The specific program is available on LinkedIn at https://www.linkedin.com/posts/tomaszdendura_multi-curve-collateral-framework-by-henrard-activity-7029797799818870784-C5g8/
You can contact the organizer Tomasz Dendura for the practical details.
We are now 7 weeks into 2023. Where do we stand in term of USD rate benchmarks?
LIBOR volume continue to decrease significantly. At LCH, it represent less than 30% on a weekly basis with the last two weeks even below 10%.
As reported in our recent post on USD Benchmarks: the winner for 2022 is ... Fed Funds!, Fed Funds dominate the USD landscape in nominal terms — not in DV01 weighted terms.
Figure 1: Weekly share by product types at LCH
If we look at the oputstanding amounts, the order has not changed for a year or so, with in decreasing order LIBOR-SOFR-EFFR. SOFR is closing the gap to LIBOR; LIBOR is around USD 60 trn down from more than USD 80 trn while SOFR is up to more than USD 55 trn from less than USD 20 trn a year ago. EFFR is around USD 25 trn. It seems that we approaching the date where SOFR will be above LIBOR. That date will be the final "SOFR First" date.
Figure 2: Outstanding amounts by benchmarks at LCH
We can compare the USD-SOFR derivartive volume to GBP-SONIA and EUR-ESTR. Obviously they are in different currencies and GBP and EUR attrach significantly less derivative volume in general. But the comparison is interesting as the difference in volume terms in not large. ESTR is even above SOFR in most of the weeks, except the last two weeks. For GBP, SONIA is the only significant benchmark. For EUR, there is still EURIBOR, without plan to stop it and ESTR as unique overnight benchmark. In USD, the situation is more complex with USD-LIBOR that is planned to stop in June 2023, and two liquid overnight benchmarks EFFR and SOFR — plus other less liquid benchmarks like AMERIBOR and BSBY.
Figure 3: Comparison between volume of GBP-SONIA, USD-SOFR and EUR-ESTR at LCH.
This shows that there is still some room before SOFR becomes the really dominant benchmark in USD rate derivatives.
For the first post of the new year, we have been looking at the volume traded on LCH for 2022. In notional terms, we get a maybe unexpected benchmark winner: Effective Fed Funds Rates (EFFR). For the last couple of years, the discussion has been all around LIBOR v SOFR but somehow EFFR manage to emerge as the winner. For the year 2022, the results are EFFR 37.6%, SOFR 33.3% and LIBOR 29.2% (we ignored inflation, basis swaps and VNS for the above shares). The weekly figures for the year are provided in Figure 1.
Figure 1: Weekly share by product types at LCH
The figure used are in pure notional terms, not risk/PV01 weighted. On a risk weighted scale, the results would probably be different - the LCH risk weighted figure are not publicly available to our knowledge.
LIBOR trading almost disappeared in last week of the year to show the smallest share ever.
On an outstanding volume, the picture is very different. SOFR has increased on a regular basis and EFFR and LIBOR have trended downward. LIBOR has still the larger share in outstanding volume with around USD 60.4 trn, then comes SOFR with USD 47.7 trn and finally EFFR with 7.6 trn. The graph with the outstanding amounts is provided in Figure 2. (1) There was probably some compression activity close to year end as all outstanding volumes were down. Overall, the outstanding amount for LIBOR has been only done 25% (USD 80 to 60 trn), which sounds like a small decrease giving the expected LIBOR's disappearance in 6 months time.
Figure 2: Outstanding amounts by benchmarks at LCH
Figure 3: Weekly SOFR volume at LCH and as reported by ISDA (US regulatory figures based).
(1) Note that our outstanding amount graphs for EFFR were incorrect in some of our previous blogs. The latest values in each graph was correct but not the past values.
Added 2023-02-01: Following our blog, Clarus publish a complementary blog adding DV01 based figures. The post is available at https://www.clarusft.com/are-fed-funds-the-latest-winner-from-benchmark-reform/. They confirmed our finding on a pure volume basis. On a DVO1 weighted basis, the picture is very different with SOFR dominating EFFR. Note also that on a DV01 weighted basis, the highest SOFR volume was in March 2022 and the trend has been slightly downward since.