Wednesday, 19 January 2022

SOFR in the second week of 2022: slow progress, still "SOFR Third" for OTC

A quick look at the OTC and ETD sides of SOFR for the second week of 2022.

The OTC Cleared at LCH side still reports a "SOFR Third" week. The major change since last week has been the change in First, now going to EFFR slightly ahead of LIBOR. SOFR's share has slightly decrease from 14.8% down to 14.6%. The figures are: OIS-EFFR 41.9%, IRS-LIBOR 37.7% and OIS-SOFR 14.6% (plus some basis, FRA, inflation). We have added the SOFR share at LCH in Figure 1 as the yellow lines (only for 2022 as we have not collected the relevant data in 2021).

Note that the ISDA figures report only LIBOR and SOFR (in particular not EFFR) and is based on US regulatory figures, which is well below LCH figures (dark blue line in the graph, around 30% of LCH volume). The SOFR share around 20% reported by ISDA is inflated due to the absence of the EFFR volume.

Figure 1: OTC SOFR volume and share of SOFR

On the STIR futures at CME side, there is a "shift in liquidity", but still very slow. The figures are LIBOR-3M 69.7%, SOFR-3M 18.5%, EFFR-1M 9.4%, SOFR-1M 2.2%, and BSBY-3M 0.2% as displayed in Figure 2. The open interest for ED has increased by 235K since 31 Dec (from 11,237,037 to 11,472,753), so the ED volume is not "risk reduction". The shares in volume have to be compare with previous shares; if we look at the December figures, we had LIBOR-3M 81.3%, SOFR-3M 10.8%, EFFR-1M 6.5%; SOFR-1M 1.1%, and BSBY-3M 0.2%. Like in the OTC case, the increase in EFFR share is interesting. The "shift in liquidity" is from LIBOR but not all to SOFR, as a large share of the shift goes to EFFR.

Figure 2: Daily STIR futures volume at CME

Some news in other currencies at LCH:


EURIBOR still largely dominant with EURIBOR (IRS+FRA) at 79.1% and ESTR-OIS at 18.5% (plus some basis and inflation).


Still some LIBOR trades (from swaption exercise), but now at 0.02% of the market! SONIA at 95.7% and inflation at 4.2%.

See also our post related to the 2022 first week: First week of 2022 at LCH - another "SOFR Third" week.

Monday, 10 January 2022

First week of 2022 at LCH - another "SOFR Third" week

One week in the new year. One week where it is recommended not to use USD-LIBOR for OTC derivatives. From the figures published by LCH, this is far from being the case. This is not dissimilar to what is happening with the futures, as described in a previous blog: SOFR Futures: LIBOR dominates!

The OTC derivatives podium, from Gold to Bronze, is LIBOR IRS 41.3%, EFFR OIS 39.8% and SOFR OIS 14.8% (the rest is basis, LIBOR FRA and inflation). Even in the OIS category, SOFR is less than one third of the market.

The absolute figures for SOFR are provided below. The ISDA Swap Info for the first week of 2022 was not available at the time of writing this blog.

Saturday, 8 January 2022

SOFR Futures: LIBOR dominates!

The title of the post may look like a typo, but it is not. For the first days of the year, among the STIR futures settling against SOFR, the ones with a LIBOR name still dominate. The post-June 2023 LIBOR futures will be converted around June 2023 into SOFR futures (with a known spread of 26.161 bps). The final settlement of those is thus SOFR based, even if they still have a name with Eurodollar LIBOR.

The total volume for STIR futures at CME was for the first week of 2022, 75.1% for LIBOR (3M), 14.2% for SOFR (3M), 8.1% for EFFR (1M), 2.1% for SOFR (1M) and 0.5% for BSBY (3M).

But if we are looking only at the post 2023 futures, they all are SOFR (3M) delivery futures (except a couple of hundreds trades on BSBY). For those trades, the LIBOR futures had yesterday (2022-01-07) a volume of 91.1% (trades up to Dec 2028) and the SOFR futures a volume of 8.9% (trades only up to Dec 2027). Hence the oxymoronic title to this blog.

The LIBOR volume does not correspond to risk reduction as the LIBOR Open Interest have increased by 100,000 contracts since 31 December 2021.

We don't know why such a trading pattern exists, but we conceive that it could be a way to hide the complexity of the new product behind an old name.

Note that on the cleared side, LCH indicates for the first week of 2022 43% IRS (LIBOR) and 57% OIS (SOFR and EFFR). The split between SOFR and EFFR is not published yet but it looks very likely that we are not yet at SOFR First.

Wednesday, 5 January 2022

USD STIR Futures in 2022

On the STIR Futures side for the first two days of 2022, LIBOR still dominates as shown in the graph below. LIBOR futures are around 81% and SOFR futures (1M + 3M) at 15.5% (the rest is EFFR 3.2% and BSBY 0.2%).

What is interesting also on the LIBOR futures side is that the split between the pre-June 2023 and post-June 2023 is roughly 50/50. Even for the post-June 2023, LIBOR is still the dominant futures, even if LIBOR will not exist anymore at that date. The market prefers to trade LIBOR futures that are planned to convert into SOFR futures to trading the SOFR futures directly.

The transition from LIBOR futures to SOFR futures is far from being trivial from a risk management and model validation perspective. There are at least three elements that should be validated before continuing trading the LIBOR futures with post-June 2023 expiry.

  • Fallback: trading post-June 2023 expiry rely on a fallback procedure. The fallback will convert LIBOR futures into SOFR futures with a price adjustment at an uncertain date (the date for GBP-LIBOR futures was mid December 2021). That procedure needs to be validated.
  • Convexity: The convexity adjustment between forward and futures is not the same for LIBOR and SOFR futures. In the LIBOR case, there is an extra market quantity, the spread between LIBOR and SOFR (used for forwards collateral); in the SOFR case, the payoff is of Asian type with the final settlement at the end of the period based on some average (composition).
  • Tenor: The LIBOR futures are based on LIBOR-3M with standard tenor convention (modified following); the SOFR futures are based on IMM dates and can have tenors between 12 and 14 weeks.

If you are trading LIBOR futures or SOFR futures, maybe a new model validation for the valuation and risk management of those instruments would be appropriate. If this is the case, don't hesitate to contact us. We have researched, published articles and developed related libraries. We can provide a rapid access to the foundations required to the assessment and validation of those market changes.

SOFR - LIBOR / Last weeks of 2021 + first days of 2022

2021 came to an end. What about LIBOR and SOFR?

SOFR certainly did not come to an end. The volumes continue to increase. LIBOR did not come to its end either. On the week before its announced demised, it still dominate the USD interest rate market.A couple of days ago, we published some figures for the USD STIR futures at CME. LIBOR was still around 80% of the market and SOFR coming second with around 14%.

LCH and ISDA have now published their numbers for the last week of 2021.

As expected, over the last 2 weeks of the year the general transaction volume was a lot lower than in the previous weeks. This is reflected in both LCH and ISDA figures. On a relative basis, SOFR is now in the ISDA figures (US regulatory figures) at around one third of the market. Still not at the SOFR First mark, but coming closer. It is difficult to assess if this is a US only effect or a global effect.

Early 2022 figures at LCH indicate that OIS (SOFR and EFFR) is around 72% of the market while IRS (LIBOR and BSBY?) is around 23% (the rest is basis, LIBOR-FRA, inflation). The split between SOFR-OIS and EFFR-OIS is not published on a daily basis. We will have to wait the weekly statistics to see it. But there are early indication that this week could be the first week of the real "SOFR First" for the cleared market.

Monday, 3 January 2022

USD Rate Futures: LIBOR still dominates!

The end of year numbers indicate that LIBOR is still by far the dominant short term interest rate (STIR) futures (at CME).

Over the last week of 2021, which is supposed to be the last week of LIBOR we have LIBOR 3M 79.1%, SOFR 3M 13.1%; EFFR 1M 6.2%, SOFR 1M 1.0% and BYSBY 3M 0.6%

Early trends for the first business day of 2022 indicate a 2022 start similar to the 2021 end.

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.