New publication: Bond futures: Delivery Option with Term Structure Modelling

We are pleased to announce a new working paper titled

Delivery Option with Term Structure Modelling

is available in our muRis_Q Advisory Model Development series of research papers. The paper is available on SSRN preprint repository at http://ssrn.com/abstract=4542275.

Abstract

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.

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The paper has been submitted for publication in an international peer-reviewed journal.

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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 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).

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 muRis_Q Advisory Model Development series of research papers. The paper is available on SSRN preprint repository at http://ssrn.com/abstract=4461418.

Abstract

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.

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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.

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.

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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.

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 muRis_Q Advisory Implementation Notes:

Swap Rates and Term Structure Modelling

The paper is available on SSRN

https://ssrn.com/abstract=4438524.

Abstract

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.

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Don't hesitate to contact us if you require advisory services related to interest rate modelling.

CEETA Benchmark Congress

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.

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Marc's presentation will be divided in two parts

SOFR - USD LIBOR transition: where do we stand?

and

LIBOR transition: what could we have done better from a quantitative perspective.

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Don't hesitate to contact us if you require advisory related to the benchmark transitions.

CCP Basis - Large LCH-EUREX basis - not unexpected

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:

Eurex-LCH basis hits new highs amid rates vol

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.

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Don't hesitate to contact us if you are interested by independent advise related to market infrastructures, initial margins and interest rate markets.

SOFR First, the next (but not yet final) step!

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

• the first day/week where there were more notional on SOFR OTC transactions  than LIBOR transactions,
• when SOFR transactions represented more than 50% of the IR OTC derivative market, 
• the last date/week when notional on LIBOR transactions was higher than SOFR transactions
• the first day/week where there were more notional on SOFR ETD/futures transactions than LIBOR transactions,
• etc.

Now it seems we have reached the next "SOFR First" moment (see Figure 1):

the outstanding notional on SOFR-linked derivatives at LCH is higher than the outstanding notional on LIBOR-linked derivatives

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).

Workshop multi-curve - Warsaw 23-24 March

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.