Thursday, 18 August 2022

SOFR: slowly getting to SOFR First

More than 5 years after the "Future of LIBOR" speech, almost 18 months after the announcement of the definitive LIBOR dismissal and more than one year after the SOFR First announcement; LIBOR is still traded in huge amounts. Only for last week LCH cleared IRS, there was 1.3 trillions USD traded.

But we see a slow progress. LIBOR volumes and outstanding notionals are slowly trending downward with some ups and downs; SOFR volumes and outstanding notionals are slowly trending upward with some ups and downs.

Figure 1: Weekly share by product types at LCH

Speaking of outstanding amount, the SOFR outstanding amount at LCH has decrease last week by 895 billions, the highest decrease ever. Nothing to be afraid of as there is a lot of short term products and they come naturally to maturity. But it may mean that we are approaching the "SOFR" peak. Note also that in term of outstanding amounts, SOFR is still well behind LIBOR with a 40 v 74 (trillions) score.

Figure 2: Outstanding amounts by benchmarks at LCH

Note that the "CME Conversion for USD LIBOR Cleared Swaps" rules have just been published. It means that since 2017, the market has been trading instrument linked to LIBOR, knowing that LIBOR would disappear and is only learning now what it has been trading for the last 5 years! Not a big success in term of transparency.

Monday, 1 August 2022

SOFR: holiday and recession

It is difficult to get a clear message from a market which is half in holiday and half in recession. From the SOFR market, we could say, once more, nothing special to say.

The share of SOFR in the LCH cleared OTC IR market is playing ups and downs around one third of hte market. The changes are as much related to LIBOR and EFFR as to SOFR. The current SOFR share is not very different from the one mid-March.

Figure 1: Weekly share by product types at LCH

On the absolute volume, the holiday mood is clear, with the current weekly volume at merely 62% of the mid-June volume.

Figure 2: Weekly SOFR volume at LCH and as reported by ISDA (US regulatory figures based).

On the subject of LIBOR transition, we looked at the outstanding notionals at LCH in the different currencies. We noticed again a relation between the transition to overnight rates and the total outstanding notionals. Since the beginning of the year, all the currencies that have fully transitioned (GBP, CHF, JPY) have seen significant decreases (GBP -15%, JPY -42%, CHF -37%), the currency that has half transitioned (USD) is almost stable (+3%) and the currency that has not transitioned at all (EUR) has seen a significant increase (+19%). The origin of this relation is not clear. It can be completely random, or it can be that the end users have decrease their risk management program as the new overnight world does not fit their needs, or it can be something else. But certainly a trend to check in the future.

Tuesday, 26 July 2022

Swap Rates and Term Structure Modelling: Implementation

Swap rate dependent products, e.g. CMS, have a long history in interest rate modelling. They look simple as only one rate is involved, but when the rate is not paid in a natural way, i.e. not according to its own annuity, they involve some type of "convexity" or "timing" adjustment.

Those products are often priced using "replication", but to do so, some approximation of the annuity discounting, or absence thereof, is used. This type of single factor approximation is what we used in our recent paper on pricing cash settled swaption through the fallback published this month in Risk (Henrard (2022)).

A very recent paper Bang and Daboussi (2022) is proposing a new approach to price swap rate dependent products in a way that preserves the full marginal distribution of all the swaps and a user selected copula between those rates.

The implementation is not trivial from a quantitative finance perspective (two changes of measure) and implementation (Monte Carlo). But by the way the numerical approach is cleverly designed, the simulations are not too costly and converge quickly.

We have adapted the methodology proposed by the authors to take into account conventions (accrual factors not all the same and the T+2 payment/effective date) and implemented it in our library. This is the library we use for consulting and model validation purposes.

The results we have observed are very good. In their paper, the authors compare the (input) market smile to the (output) model generated smile for vanilla options and find a very small discrepancy, i.e. the numerical noise is small on the present value. We have obtained the same results. We have also done the comparison for the smile risk which was not presented in the paper. We computed the sensitivities to the alpha, beta, rho and nu parameters in a SABR model. In our implementation, the sensitivities are obtained by Algorithmic Differentiation (AD) as you would expect. For a 2Yx5Y swaption, here is the comparison between the analytic result (direct formula for the vanilla) and the Monte Carlo with AD version:

As you can see, the numerical noise is below 0.05% of the actual number on the alpha-vega (a little bit higher for nu and rho). This was obtained with a relatively low number of Monte Carlo paths (1,000).

Why we are interested by this approach, beyond its natural application to CMS, is for the above mentioned fallback of cash settled swaptions with the LIBOR-linked swap rate discontinuation.

With a precise view of the term structure smile risk in CMS-like products, we can now have a look at term structure smile risk for the fallback. That will be the subject of a forthcoming blog.

Henrard, M. (2022). Swap rate: cash settled swaptions in the fallback. Risk, Cutting Edge. Published online 1 July 2022.

Bang, D. and Daboussi, E. (2022). Modelling of CMS-linked products in an RFR framework, with extension to hybrids, forward starting and canary options. SSRN 4134438.

Don't hesitate to contact us if you are interested by model developments or model validation related to swap rate linked products like CMS.

Monday, 25 July 2022

LIBOR Transition: Back to "LIBOR First" - again!

Same title as 3 weeks ago!

LIBOR is again the first benchmark in USD this week at LCH!

Figure 1: Weekly share by product types at LCH

Wednesday, 20 July 2022

LIBOR, EFFR and SOFR still playing yo-yo!

USD-LIBOR trading should have stopped more than 6 month ago, but in the market figures there is still large activity around it. From week to week, the dominant benchmark in the USD derivative market change from LIBOR to SOFR to EFFR. Last week the winner was EFFR, the week before it was SOFR and another week before is was LIBOR.

Figure 1: Weekly share by product types at LCH

We are still far away from a all-in in SOFR; maybe we will never go there!

Figure 2: Weekly SOFR volume at LCH and as reported by ISDA (US regulatory figures based).

Wednesday, 13 July 2022

Getting closer to SOFR First!

Getting closer to SOFR First! The SOFR share at LCH was last week at 43.7%, highest share and getting closer to 50%.

Figure 1: Weekly share by product types at LCH

Note that there is no more LIBOR swaps outstanding at LCH in GBP and JPY. We had to wait July to make such an announcement as the last LIBOR-6M, fixed at the end of December, were paid at the end of June (GBP, T+0) and beginning of July (JPY, T+2). In CHF, there is still CHF 30 millions of LIBOR swaps outstanding; this is probably a LIBOR-12M swap with one coupon still to be paid.

Tuesday, 5 July 2022

LIBOR Transition: Back to "LIBOR First"

For the first time in a while, we are back to "LIBOR First" at LCH and for US regulatory figures.

Figure 1: Weekly share by product types at LCH

The story told by the ISDA published US regulatory figures is similar (see Figure 2). For those figures also, LIBOR is back to the fore. This can be seen with the ratio SOFR outright/(LIBOR+SOFR) which is back below 50%.

Figure 2: Weekly SOFR volume at LCH and as reported by ISDA (US regulatory figures based).

There are more and more discussion about allowing a wider use of the SOFR Term rate. This is based on its usage in cash products. Derivatives are (or at least should be) designed to help risk management. If derivatives cannot be based on the same underlying benchmark as the cash product, they become less useful. This is the case for Term Rate based swaps but also optional products like cap/floor. Some cash products have explicit or implicit cap or floor, but currently they cannot be hedged easily in the wholesale market.

Issues regarding the SOFR Term rate itself can also been seen in Figure 2. The short term part of the SOFR-OIS (less than 2 year) is not large. This means that it is difficult to established a term rate based on liquid regulated electronic trading venues (Level 1 waterfall). We have mentioned this issue in several blogs and presentation (see here for example). Currently, CME SOFR Term rate is based on level 3 of the waterfall (futures) and IBA SOFR Term rate is based on level 2 of the waterfall (dealer to client). Also when using futures, creating the term rate requires some arbitrary interpolation scheme choice and has some timing issue.

With only one year to go to the LIBOR end date, this is not very good for the transition!

Sunday, 3 July 2022

Published paper: Swap Rate: cash settled swaptions in the fallback

The paper on the swap rate fallback and its impact on cash-settled swaptions announced in March has now been published in Risk.

Swap Rate: cash settled swaptions in the fallback

The paper is available on the Risk web site at


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.

One graph from the paper: Error between replication with annuity ratio and order 2 approximation.

Sunday, 26 June 2022

USD STIR Futures: SOFR progress ... but still too much LIBOR

We are six months into the "now new USD-LIBOR risk traded" period as announced by regulators. We had a look at the situation through the eyes of the STIR futures market at CME.

USD-LIBOR futures have been the most liquid STIR futures for many years. The new SOFR futures and the "SOFR First" initiatives should have shifted the volume.

In Figure 1, the daily volume at CME is displayed. One can see that SOFR-3M futures have now a higher volume than LIBOR-3M futures. But this is a recent phenomenon that appeared only in May and the advantage of SOFR is small. Over last (short) week, the SOFR volume as only 20% higher than the LIBOR volume.

Figure 1: Daily STIR Futures volume at CME.

On the open interest side, LIBOR is still largely above SOFR with an excess OI of 75%. More details are displayed in Figure 2. Moreover LIBOR OI as only decreased slightly since the start of the year, from 11.2 m contracts to 9.6 m (-16%). A large part of the decreased came when existing contracts came to expiry. Since the beginning of the year, the total LIBOR futures volume has been 265.8 m contracts. The decrease in OI correspond to 0.7% of the traded volume. We are extremely far away from a situation were the new LIBOR trades are risk reducing!

Figure 2: Open Interest in STIR Futures.

Another feature of the futures market is the expiry date of the contracts traded. LIBOR with cease in June 2023. One could claim that trading LIBOR contracts with expiry before that date make sense from a risk management perspective and is in line with the spirit of the SOFR first requirement in the sense that those trade do not add to the transition effort which is not needed before June 2023. But the expiry profile of the futures traded does not look like that at all. If we take the traded volume for quarterly contracts on Friday 24 June, we get a expiry profile displayed in Figure 3.

Figure 3: Daily volume on 24 June 2022 for the different quarterly expiries.

The SOFR-3M futures are dominating overall, but for the maturities beyond June 2023, LIBOR is dominating. The higher LIBOR volume is even more important on a relative basis for longer expiries. If we take contracts with maturity beyond 5 years (June 2027 and beyond), the LIBOR volume is 27 times higher than the SOFR volume. Is there some market participants betting on the transition not taking place in the next 5 years?

This leads to a question we have asked for some time, without finding an answer. Or more exactly finding plenty of answers, but all bad (and scary) answers. The question is

Why do financial institution still trade LIBOR futures/swaps?

In the different seminars on SOFR that we are presenting, we use the following slide to put the question in perspective.

Figure 4: Why do financial institution still trade LIBOR futures/swaps?

  • Investment universe. SOFR products not approved by the investment committee.
  • Validation Model. validation had no time to do a full validation of the new products.
  • Systems. The system (risk/accounting) cannot cope with the SOFR products / the composition in-arrears.

Those reasons are valid reason from a very short term practical perspective, but certainly not valid 5 years after the "Future of LIBOR" speech by FCA, 4 years after the creation of SOFR and 1 year after one knows about the actual cessation date. It can take time to change systems, guidelines and validate changes. But by trading LIBOR products, you are only lying to yourself and hiding your weakness to yourself, not solving any of them. At the very least I would expect participants to trade the real think (SOFR swaps and futures), without frankensteins-like fallback, and book/report them in the best way they can. That could simply be to create swaps/futures linked to SOFR term rate (same system complexity as LIBOR) and adjust the booking as soon as possible. At least you will represent the bulk of your risk correctly and link it to SOFR!

Don't hesitate to contact us for advisory work related to the transition, the associated model developments, validation, or implementation.

Wednesday, 15 June 2022

ESTR: Volume and term rate

This week, SOFR as usual (small progress) but important news on the ESTR side. EMMI (the administrator of EURIBOR and the disappeared EONIA) has started to publish a ESTR Term rate (in beta version).

The Term rates are unfortunately not part of the fallback in the derivative ISDA definition but the Euro Risk Free Rates Working Group has recommended a forward-looking term rate as a fallback for EURIBOR for certain asset classes.

This new step in the direction of a term rate is accompanied by an important surge in the ESTR-OIS volume as can be seen in Figure 1. The weekly volume was around USD 6.8 trillions. By comparison SOFR volume was around USD 3.2 trillions, less than 50%.

Figure 1: Weekly ESTR volume at LCH.

As described in several SOFR related blogs and seminars (e.g. here), the share of the ESTR short term trades (in gray in Figure 1) is quite high. The ESTR liquidity is concentrated where it is important to have a robust ESTR Term rate. This is by opposition to USD-SOFR where only a small part of the volume is short term and the recommended SOFR Term rate is based on futures which require an arbitrary interpolation schemes and un-hedgeable time weights.

Also in relative terms, ESTR is taking more importance. As displayed in Figure 2, the ESTR share has reached 60% last week, to be compared with SOFR share at 37%.

Figure 2: Weekly share by product type at LCH.