Monday 29 May 2023

LIBOR to SOFR conversion at LCH: one week on

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).

Sunday 28 May 2023

New publication: Swap Rates Fallback and Term Structure Modelling

We are pleased to announce a new working paper titled

Swap Rates Fallback and Term Structure Modelling

is available in our muRisQ Advisory Model Development series of research papers. The paper is available on SSRN preprint repository at


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.

Tuesday 23 May 2023

US - Eurodollar futures a USD 8 million rounding error

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.

Publication: LIBOR: le chiffre le plus important du monde disparaît

Marc a publié un article de vulgarisation sur la disparition du LIBOR dans le magazine EcoFin Mag (ECOFINMAR n 15 - mars 2023, page 32). L’article est intitulé

LIBOR: le chiffre le plus important du monde disparaît.

Une copie de l’article peut être obtenue ici.

Sunday 7 May 2023

Swap Rates and Term Structure Modelling: Implementation note published

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:

Swap Rates and Term Structure Modelling

The paper is available on SSRN


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.