Curve calibration and LIBOR-OIS spread

With the different transitions taking place in the interest rate markets, the spreads between the different rates have never been discussed so much. In USD, the USD-LIBOR/SOFR spread is important for the fallback expected at the start of 2022 and the EFFR/SOFR spread is important for the discounting and PAI big bang expected in October 2020.

In this post, we discuss the LIBOR-OIS spread; an analysis of the discounting transition has been presented in a previous post titled Change in collateral rate at CCP: quant perspective. The analysis presented here is largely inspired by Section 5.12 of Henrard (2014) and adapted with recent data and to the current situation. We focus on the USD market.

When building the overnight curve, it is important to take into account the actual market behavior for overnight fixing. The general shape of the historical time series is a set of period with (roughly) constant overnight rate between two FOMC dates and jumps at those dates.

A typical curve calibration procedure to match this shape is to build a curve with log-linear interpolation on the discount factors - to get the piecewise constant overnight rates - and with nodes on the FOMC dates - to get the jump dates correct. The market data input can be standard monthly OIS. The result of such calibration as of 21 June 2019 is provided in the figure below. Each circle is a projected overnight rate starting at the date indicated by the date on the X-axis.

Figure 1: Overnight forward piecewise constant between FOMC dates.

Then we want to calibrate the LIBOR curve. A typical approach for the LIBOR curve is to take the preferred interpolation mechanism and calibrate to liquid market instruments. In the example below, we have used linear interpolation on zero rates and a curve based on FRAs up to 9 months and IRS from 1 year on. Figure 2 represents the projected forward LIBOR-3M rates obtained from this method.

Figure 2: Forward LIBOR-3M rate obtain from linear interpolation on zero-rates (blue) and implied forward looking OIS rates on the LIBOR periods (red).

Obviously those two items (OIS and LIBOR) are not independent of each other; the spread between LIBOR rates and forward looking OIS rates based on overnight benchmarks is an important market information. This is why in Figure 2 we have also displayed the forward OIS rate implied by the curve on the same periods as the LIBOR rates.

We are now in a position to compute the spread between those two rate types. The spread obtained with the above methodologies is displayed in Figure 3. The dark blue circles are the spreads obtained for each date.

Figure 3: LIBOR-3M/OIS spreads for a LIBOR curve build outright (dark blue) and as a spread (gray); linear interpolation on zero-rates.

The methodology described above is not the only one possible. Another approach, which technically implements the intuition that (forward looking) LIBOR and (forward looking) OIS rates have a lot in common, is to build the LIBOR curve as a spread to the OIS curve. In the example we have implemented for this post, we use the OIS curve with piecewise constant overnight rate between FOMC meeting, view it in term of zero-rate and add an interpolated zero-rate on top of it to represent the spread. The resulting implied LIBOR/OIS spreads are displayed in gray in Figure 3. For that figure, the interpolation on the zero-coupon spread is the same as the one selected for the LIBOR curve before, i.e. linear. Some of the spread spikes have been reduced. The spreads are looking more natural.

Figure 4 and 5 display graphs similar to the one in Figure 3, but with different interpolation mechanisms for the LIBOR curve. In Figure 4 the log-linear interpolation on discount factors is used and in Figure 5 the natural cubic spline interpolation on zero rates is used.

Figure 5: LIBOR-3M/OIS spreads for a LIBOR curve build outright (dark blue) and as a spread (gray); product linear interpolation on zero-rate (equivalent to log-linear on discount factors).

Figure 5: LIBOR-3M/OIS spreads for a LIBOR curve build outright (dark blue) and as a spread (gray); natural cubic spline interpolation on zero-rate.

In this post, we don't claim that any of the above method is perfect ans superior to all others. Our claim, like for any feature related to curve interpolation, is that any interpolation mechanism is a hypothesis and represents our ignorance, our lack of information between the points we interpolate. Using different approaches based on different views of the same issues can only increase our confidence that we understand impacts and pinpoint our attention where our hypothesis have an unexpected impact. The spread curve approach for LIBOR is certainly a tool that market-makers or arbitrageurs with a significant exposure to spreads want to have in their arsenal.

ISDA Consultation on IBOR fallback: GBP impacts

The results of the final consultation on parameters and tenors had been published on Friday 15 November 2019. The decision is to use "historical median approach over a 5-year lookback period" with "two banking day backward shift adjustment period".

Based on the median and 5-year lookback period, we have recomputed our estimations for the LIBOR-SONIA spreads in GBP. The two graphs below are for the LIBOR-3M and the LIBOR-6M. The LIBOR-6M/SONIA spread is obtained by combining the more liquid LIBOR-6M/LIBOR-3M and LIBOR3M-SONIA spreads.

The graphs contain the historical data for LIBOR-SONIA basis swaps with a tenor of 30-year (dark blue line) and with a tenor of 1-year (light blue line). The vertical red lines correspond to the consultations important dates: start of the first consultation in July 2018, publication of the results of the first consultation on 26 November 2018, spread consultation start on 19 September 2019 and the spread consultation results on 15 November 2019. Both the LIBOR-3M and LIBOR-6M spread to SONIA have moved considerably after Friday's results.

The grey lines represent the estimates of historical spreads using different methodologies. Between the first consultation results and the spread consultation publication, we have used 5, 7 and 10-year periods and both median and mean (light grey) in all cases with different announcement dates. Between the the spread consultation publication and its results, only two scenarios were still under discussion: the 10-year period with mean (middle grey) and the 5-year period with median (dark grey). From Friday onward, only this last scenario is still of interest.

Figure 1: Market (1-year and 30-year) and historical spread for LIBOR-3M/SONIA.

Figure 1: Market (1-year and 30-year) and historical spread for LIBOR-6M/SONIA.

We can see that in both cases, the market spread for 30-year tenor moved to the 5-year period median values. The market spread for 1-year tenor seems unaffected. From our computations, we see still some room for the LIBOR-3M/SONIA spread to narrow by a couple of basis points.

All the figures above are for cleared swaps. The impacts on uncleared swaps need to be reviewed separately.

IBOR Fallback status for different products:

We have proposed many detailed technical documents related to the IBOR fallbacks. Beyond those important details, one overview question reappear on a regular basis: what is the status for the different vanilla products (cleared and uncleared).

Below is our summary answer.

First a couple of definitions:

ISDA new fallback: compounding setting in arrears with 2 days composition period shift and historical median over 5-year lookback period.

CCPs new fallback: ISDA new fallback, once and how adopted by the CCPs (small variations possible).

New trades: Trades done after the introduction of the new definitions (expected in 2020).

Vanilla IBOR swaps

• Cleared
• Legacy and new trades: CCPs new fallback
• Uncleared
• Legacy trades: Current fallback no fit for purpose, possibility to sign protocol to use ISDA new fallback. Cost of signing the protocol to be determined (see short story and Quant Insights 2019 presentation). New fallback changes the forward rates (fixed spread).
• New trades: ISDA new fallback.
• Note: For some almost vanilla swap, like IMM swaps, the ISDA fallback is not achievable for all coupons, even with the 2-day composition period shift. For those trades (legacy and new), fallback to be agreed bilaterally.

FRA

• Cleared: New ISDA fallback not fit for purpose, fallback at the sole discretion of the CCPs, no mechanism proposed yet.
• Uncleared:
• Legacy and new trades: New ISDA fallback not fit for purpose, to be agreed bilaterally.
• Alternative: Physical settled OIS (see description here)

Cap/floor

• Cleared: not cleared at any CCP
• Uncleared:
• Legacy trades: Current fallback no fit for purpose, possibility to sign protocol to use ISDA new fallback. Cost of signing the protocol to be determined. New fallback changes the forward rates (fixed spread) and the option type (European to Asian)
• New trades: Asian options instead of European
• Alternative term sheet for new trades (potentially for legacy trades with a new protocol): European options with physical settled OIS (see description here)

Swaptions

• Cleared: Short term optionality at CME, very illiquid. CCPs new fallback.
• Uncleared
• Physical delivery of a cleared swap: CCPs new fallback.
• Cash settlement: No fallback for the ICE swap rate, currently no solution. Note that cash settlement with collateralised price is impacted by the change of discounting mechanism at CCPs in 2020.
• Alternative: Change cash settlement with collateralised price to physical settlement at CCP. Require assessing the impact on valuation (forward, volatility, discounting).

ED futures and options

• CME: Fallback to SOFR futures, generally in line with the ISDA fallback for swaps (compounding and spread). Difference on the underlying period (IMM v LIBOR 2 days shifted). Some comments here.
• Other CCPs: no official proposals yet

 

Deliverable swap futures

• No official proposal yet
• Alternative: Create OIS risk-based futures (as proposed in white paper Risk-Based Overnight-Linked Futures Design).

---

Don't hesitate to contact us for more details on our research and tools related to the LIBOR fallback for OTC and ETD derivatives.

CME ED futures fallback

CME as published the general description of the planned fallback for Euro-dollar futures and euro-dollar options.

At a high level, CME plans to copy the ISDA fallback methodology, replacing the forward looking LIBOR by a backward looking SOFR composition and a fixed spread. The spread will be the same as the one computed according to ISDA planned new definitions. If the goal is to mimic the ISDA new definitions, it appears to us that the CME proposal is a good methodology ... in theory.

As always, the devil is in the details. Among those details are the convexity adjustment (already described in the working paper Overnight Futures: Convexity Adjustment, February 2018. Available at SSRN: https://ssrn.com/abstract=3134346) and the difference in volatility between LIBOR and OIS (Hybrid Model: A Dynamic Multi-Curve Framework, August 2018. Available at SSRN: https://ssrn.com/abstract=3237403).

Another detail that was briefly touched on in the CME webinar is the difference in period on which the rates are computed for LIBOR futures and SOFR futures. To which we have to now add the 2 business day shift in ISDA OTC LIBOR fallback.

In practice what is the magnitude of those "period adjustments"? This is one of the elements we have looked at in our analysis of the transition. The table below reproduces the disparities in days using the SOFR futures as base and the ED futures and OTC theoretical compounded in-arrears (under the hypothesis that the LIBOR period is used as reference for the in-arrears computation). We have simply displayed the figures for 2022.

Futures month	OTC start	ED end	OTC end	ED length	SOFR length	OTC length
Jan-22	-5	-1	-6	90	91	90
Feb-22	-2	-2	-6	89	91	87
Mar-22	-2	1	-1	92	91	92
Apr-22	-2	0	-2	91	91	91
May-22	-2	1	-1	92	91	92
Jun-22	-2	-6	-8	92	98	92
Jul-22	-2	1	-1	92	91	92
Aug-22	-2	1	-1	92	91	92
Sep-22	-2	0	-2	91	91	91
Oct-22	-2	1	-1	92	91	92
Nov-22	-2	1	-1	92	91	92
Dec-22	-2	6	2	90	84	88
Min (2020-2031)	-5	-6	-8	89	84	87
Max (2020-2031)	-2	6	2	92	98	95

As can be seen, the OTC start date can be between 2 and 5 days before the SOFR futures start date. The end between SOFR and ED futures is anything between -6 and 6 days. The end between SOFR futures and fallback OTC is anything between -8 and 2 days. You can also see the differences in term of accrual period length.

Obviously those difference in length means a different hedging efficiency between the current LIBOR framework and the after fallback SOFR framework.

---

The code used to produce the table above can be found (open source) on the GitHub marc-henrard/analysis repository at https://github.com/marc-henrard/analysis/blob/master/src/analysis/java/marc/henrard/analysis/fallback/FallbackEurodollarFuturesDatesAnalysis.java

---

Don't hesitate to contact us for more details on our research and tools related to the LIBOR fallback for OTC and ETD derivatives.

Final parameters fallback consultation results - updated transformers

The results of "The Final Parameters Consultation" have been published by ISDA on 15 November 2019. The fallback will be based on "historical median approach over a five-year lookback period" with "two banking day backward shift adjustment period".

We have updated our "LIBOR fallback transformers" code to include the new fallback options introduced by the consultation. Now the choice of fallback extends to the compounding in arrears with two days shift on the IBOR period or two days shift on the calculation period.

---

Don't fallback, step forward!

Contact us for LIBOR fallback and discontinuation: trainings, workshops, advisory, tools, developments, solutions.

Interest Rate Reform Conference: LIBOR transition workshop

Marc Henrard will present a workshop at

Interest Rate Reform Conference.

The workshop will take place on Wednesday 4 March 2020 in London. The details of the workshop can be found on the organizer web site:

Benchmarks and LIBOR transition: Quantitative Perspective on Benchmarks, Overnight, Libor Fallback and Regulation.

---

Workshop's overview: 

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for benchmark-linked derivatives is becoming paramount. The recent regulations include the EU Benchmark Regulation (BMR) which will have a severe impact on the EUR market from January 2022. For all major currencies, new benchmarks have been proposed and the market are in a transition phase. Each transition has his idiosyncrasies and a common transition approach cannot be expected. On the EUR side, a recalibration approach with clean discounting has been proposed for EONIA. This has happened on 2 October 2019. This changes have potentially important value transfer impacts. On the fallback side, several options have been proposed and ISDA is holding consultations on some of them. The results of the first ISDA consultations has been to select the ``compounding setting in arrears" adjusted rate and the "historical mean/median" spread approach. We present those options and emphasise their drawbacks. In particular the compounding setting in arrears lack of details and, in the words of ISDA, is not workable for some products. We also present alternative options supported by different working groups. The historical spread option can lead to significant value transfer, some of them having already taken place. The latest consultation on fallback parameters and tenors finished in October, new value transfers have been observed. We present historical data is several currencies to support the theoretical developments. The presentation focuses is on the quantitative finance impacts for derivatives. On top of this, CCPs have announced their transition plan from the current ON benchmarks (Fed Funds and EONIA) to the new ones (SOFR and ESTR). More opportunities to make or lose money if you understand the fine quantitative details of the transition or not.

Graphical representation of elements of my personal filtration related to the fallback.

---

The workshop is also offered as an in-house program tailor-made to your exact requirements in term of content and schedule.

---

Don't hesitate to reach out if you want to meet at Interest Rate Reform Conference or discuss our services.

Change in collateral rate at CCP: quant perspective

CCPs have announced that they will change the PAI/collateral rate in USD from Effective Fed Fund rate (EFFR) to SOFR. This will be done as a big bang approach, not in line will the planned paced transition set by ARRC in 2017. The planned date for the big bang transition at CME and LCH is Friday 16 October 2020. Some description for CME can be found on their website; we have not found a similar description for LCH, even if it appears that the methodology will be similar.

Such a big bang approach does not offer the "choice between clearing swap contracts into the current PAI/discounting environment or one that uses SOFR for PAI and discounting" as planned by the ARRC. The change is forced on market participants at a price and with a methodology selected by the CCPs.

Such an approach creates the opportunity for value transfer between market participants and may generate unintended consequences. We have detailed some impacts, potential consequences and open questions in a technical document now available freely on a preprint server.

The document, in the muRis_Q Advisory Market Infrastructure Analysis series, is titled

SOFR discounting transition: multi-curve and quantitative perspective.

and is available on SSRN with the reference

Henrard, Marc P. A., SOFR discounting transition: multi-curve and quantitative perspective. Market Infrastructure Analysis, muRis_Q Advisory, October 2019. Available at SSRN: https://ssrn.com/abstract=3478769.

---

Added 23-Nov-2019: The code used to create some of the PV01 reports is available (open source) on the marc-henrard/analysis Gitbub repository: https://github.com/marc-henrard/analysis/blob/master/src/analysis/java/marc/henrard/analysis/product/overnighttransition/SofrPaiTransitionSensitivityAnalysis.java

Answer to the ISDA consultation on Final Parameters for the Spread and Term Adjustments

ISDA third consultation regarding IBOR fallback closed last week. As for the previous consultation, we have provided a detailed answer. The text of our answer can be found on SSRN:

Answer to ``Consultation on Final Parameters for the Spread and Term Adjustments in Derivatives Fallbacks for Key IBORs'' issued by ISDA.

Conclusion:

The consultation asks many questions related to technical details for the IBOR fallback term. Unfortunately it does not consider the main issue, which is that the proposed base solution of compounded setting in arrears is ill-conceived. It fundamentally changes the meaning of IBOR fixing and the question and workaround related to the term are the consequence this ill-conception. Most of the questions consists of workaround for issues that have been described in detail over the last 18 months.

The spread part also focuses on narrow technical questions on how to compute it. It does not answer the question on how to prevent this computation to harm end users through the implied massive value transfer.

We suggest once more to ISDA to review the decision to base the fallback on the compounding setting in arrears and historical mean approaches.

Associated documents:

The answer should be read in conjunction with our previous answer and publication, including a couple of paper in peer reviewed journals.

1. Answer to``Consultation on Certain Aspects of Fallbacks for Derivatives Referencing GBP LIBOR, CHF LIBOR, JPY LIBOR, TIBOR, Euroyen TIBOR and BBSW'' issued by ISDA. October 2018. Available at http://multi-curve-framework.blogspot.com/2018/10/isda-consultation-on-libor-fallback-my.html.
2. LIBOR Fallback transformers! Market Infrastructure blog, muRisQ Advisory, October 2018. Available at https://murisq.blogspot.com/2018/10/libor-fallback-transformers.html.
3. A Quant Perspective on IBOR Fallback consultation results. Market infrastructure analysis, muRisQ Advisory, January 2019. Available at http://ssrn.com/abstract=3308766.
4. Answer to ``Supplemental Consultation on Spread and Term Adjustments for Fallbacks in Derivatives Referencing USD LIBOR, CDOR and HIBOR and Certain Aspects of Fallbacks for Derivatives Referencing SOR'' issued by ISDA. July 2019. Available at https://ssrn.com/abstract=3415930.
5. Answer to ``Consultation on Final Parameters for the Spread and Term Adjustments in Derivatives Fallbacks for Key IBORs'' issued by ISDA. October 2019. Available at https://ssrn.com/abstract=3476530.
6. LIBOR fallback and quantitative finance. Risks, 7(88), August 2019.
7. LIBOR: Don't fallback, step forward. Wilmott Magazine, November 2019, to appear.

Rate reform: a recognised expertise

Over the coming years, one of the main issues in interest rate trading and risk management will be the emergence of new benchmarks and the potential IBORs fallback.

In the past year, we have looked at those issues from a theoretical and from a practical point of view. Some of the theoretical issues are detailed in a note that Marc published recently called "A Quant Perspective on IBOR Fallback Consultation Results" (https://ssrn.com/abstract=3226183). Our answers to the different ISDA consultations are also available on SSRN. On the practical side we have implemented different fallback options, curve calibration mechanism and convexity adjustment to analyze the impacts on large portfolios. Some descriptions of the tools are available in a series of previous blogs.

Our expertise has been recognized by the market as documented from the invitations to many practitioner and academic finance conferences and seminars. Marc has been invited as guest speaker or expert panelist at the following events:

• The future of LIBOR (CFA Society Denmark, Copenhagen, Denmark) - 24 January 2019
• CASS Financial Engineering seminar (CASS Business School, London, UK) - 6 February 2019
• Quant Summit (organized by Risk.Net, London, UK) - 6-7 March 2019
• Singapore Management University seminar - 8 April 2019
• QuantMinds International (Vienna, Austria) - 14-16 May 2019
• CASS Business School workshop on LIBOR transition (London, UK) - 19 June 2019
• Risk Live (organized by Risk.Net, London, UK) - 27 June 2019
• LIBOR: Don't fallback, step forward (CQF Institute talk, London, UK) - 23 September 2019
• CCP round-table (organized by Risk Dynamics, Brussels, Belgium) - 10 October 2019
• The 15th Quantitative Finance Conference (organized by WBS, Rome, Italy) - 16 October 2019.
• The 5th Quant Insights Conference (organized by CQF Institute and Wilmott, London, UK) - 15 November 2019.
• The future of LIBOR (workshop at RiskMinds International, Amsterdam, Netherlands) - 6 December 2019
• Interest rate reform conference (organized by WBS, London, UK) - 4-6 March 2020
• QuantSummit Europe (organized by Risk.Net, London, UK) - 11-12 March 2020
• Interest rate reform conference (organized by WBS, Frankfurt, Germany) - 26-27 March 2020
• QuantMinds International (Hamburg, Germany) - 11-15 May 2020

We are also presenting in-house workshops on similar subjects (see our training page on LIBOR) at different financial institutions in Europe.

Don't hesitate to contact us if you want to discuss potential in-house training or providing expertise on this subject for your projects.

New benchmarks, LIBOR transition and fallback.

With the increased expectation of some LIBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for benchmark-linked derivatives is becoming paramount.

Financial institution and the end-users of interest rate derivatives face many challenges when navigating through those changes and their impacts. The impacts are far reaching and relate to not only to the legal and operational issues but also to pricing, risk, modelling, validation and implementation in systems.

muRisQ Advisory has an extensive experience related to benchmarks and LIBOR transition. We have published on the subject since more than 2 years and have modelled and implemented the impacts in theory and in practice. We have been guest speaker at major academic and practitioner conferences in the last 18 months (see partial list).

We have help institutions in this regards in several ways:

Technical workshops

• Public workshops. Planned next presentations: WBS Quantitative Finance conference (Rome, 16 October 2019), RiskMinds (Amsterdam, 6 December 2019)
• In-house tailor-made workshops on the quantitative finance impacts (valuation, risk, value transfer, model validation, new instruments). Typical agenda available on our training page.

Independent impact assessment

• We use our own production grade systems developed over the last years
• Run existing different hypothesis for fallbacks and spreads on exiting portfolios
• Analysis of re-papering and protocols impacts
• Analysis of value transfer on actual portfolios

Implementation advisory

• Support of quantitative analysis and risk groups in implementation (based on more than two years of internally developed research and systems)
• New models development
• Senior stakeholder support
• New exchange traded products development
• Reduction of existing exposure
• Support for negotiation with counterparties

RiskMinds International: The future of LIBOR workshop

Marc Henrard will present a workshop at

RiskMinds International 2019.

The talk will take place on Friday 6 December 2019 in Amsterdam. The details of the workshop can be found on the organizer web site:

RiskMinds International: The future of LIBOR workshop.

We can offer you a 10% speaker discount for RiskMinds. Contact us to obtain the code.

---

Marc's workshop, will be titled The future of LIBOR.

Workshop's overview:
With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for benchmark-linked derivatives is becoming paramount. The recent regulations include the EU Benchmark Regulation (BMR) which will have a severe impact on the EUR market from January 2022. For all major currencies, new benchmarks have been proposed and the market are in a transition phase. Each transition has his idiosyncrasies and a common transition approach cannot be expected. On the EUR side, a recalibration approach with clean discounting has been proposed for EONIA. This will happen as soon as 2 October 2019. This changes have potentially important value transfer impacts. On the fallback side, several options have been proposed and ISDA is holding consultations on some of them. The results of the first ISDA consultations has been to select the ``compounding setting in arrears" adjusted rate and the "historical mean/median" spread approach. We present those options and emphasise their drawbacks. In particular the compounding setting in arrears lack of details and, in the words of ISDA, is not workable for some products. We also present alternative options supported by different working groups. The historical spread option can lead to significant value transfer, some of them having already taken place. We present historical data is several currencies to support the theoretical developments. The presentation focuses is on the quantitative finance impacts for derivatives.

October 2019 update: ESTR has now been published since 2 October and EONIA re-calibrated to ESTR+8.5bps. New consultation on fallback parameters and tenors have been issued, new value transfers have been observed. On top of this, CCPs have announced their transition plan from the current ON benchmarks (Fed Funds and EONIA) to the new ones (SOFR and ESTR). More opportunities to make or lose money if you understand the fine quantitative details of the transition or not.

Graphical representation of elements of my personal filtration related to the fallback.

---

Don't hesitate to reach out if you want to meet at RiskMinds.

CQF Institute: LIBOR - Don't Fallback, Step Forward

Marc Henrard will speak at the

CQF Institute.

The talk will take place on Wednesday 18 September 2019 in London. The details of the talk can be found on the organizer web site:

CQF Institute talk.

---

Marc's talk, will be titled LIBOR - Don't Fallback, Step Forward.

Talk's overview:
With the expected discontinuation of the LIBOR publication, a robust fallback for related derivatives is paramount. In recent months, several consultations have taken place on the subject. To the author's point of view, the proposals are not satisfactory. In this talk, we describe why the main proposal is not achievable in practice and a fundamental revision of the fallback's foundations is required. The talk will then focus on the value of transfer coming from the adjustment spread computation. Part of the transfer has already taken place and more will take place in the future. The source of the value transfer is analysed. A quantitative analysis of the spreads is provided and compared to recent market movements.

---

Don't hesitate to reach out if you want to meet after the talk.

Presentation at Cass Business School - Planning for the end of LIBOR

Marc Henrard has presented a seminar at the conference

Planning for the end of LIBOR

organized by Cass Business School in London on Wednesday 19 June 2019.

The conference was well attended with more than 200 people registered.

Copyright © 2019 by Cass Business School

Introduction to the presentation

Copyright © 2019 by Gianluca Fusai

Marc explaining the intricacies of the fallback spread calculation and its impact on today's valuation.

Change in collateral rate - fair compensation

The transition from EFFR to SOFR as collateral rate has an important impact in term of valuation. This change is very different from the change from LIBOR discounting to OIS discounting. The LIBOR/OIS discounting was a change of valuation formula from one that was used up to then to a new one that the users though was better. It was a correction of an internal valuation process but there was not change in the term sheet of the products. The pay-off were unchanged. No compensation was required.

The collateral transition is a very different prospect. In this case, the term-sheet of the trade, through its CSA - uncleared trades - or rule book - cleared trades -, is altered and the pay-offs, at least the ones associated to the payment of interest on the VM are changed. That change of term-sheet requires a compensation.

In the uncleared work, the compensation scheme has to be agreed by both counterparties to the trade. In the CCP world, the clearing house is the calculation agent and they may have the right to do the change at their own conditions, but there is still an expectation that this will be done in a fair way for each participant. The compensation for the change of collateral rate is not a standard variation margin for which the exact formula has a small impact; this is a fundamental transfer of value. It has to be computed very precisely and is a definitive value transfer.

The change is composed of two parts: The change of level between the two rates and the specific details of the rate on each day. Historically the difference between SOFR and EFFR has been a couple of basis point on average, with SOFR higher than EFFR. That difference is reflected into the basis swap for SOFR v EFFR. The change due to daily idiosyncrasies and intra-month seasonality is more complex. The quoted rate are for monthly or even yearly periods; the liquid market does not provide information about single days. Moreover, a good forward curve should replicate the shape of historical data with steps between FOMC meetings and on top the intra-month seasonality for SOFR.

In this note we concentrate on the intra-month seasonality. We suppose that the difference of average level has been taken into account and does not need to be look at anymore.

Methods to incorporate the seasonality in the curve was described our recent blog Fed Funds to SOFR: Impact of seasonality. In this blog we look at the monetary impact of that seasonality. By definition, on average the impact is null. But that impact will be spread between the different parties in a different way and some parties may be advantaged by the methodology selected. Some parties may position themselves in such a way to take advantage of the transfer.

Historically the SOFR rates have been higher on month end, in the first days of the month and around the 15th of the month. We create positions with a total PV01 equal 0 but with an impact on the value due to expected idiosyncratic spikes. The impact on value is estimated by valuing the portfolios with one forward curve including the seasonality and one without seasonality.The seasonality we use for this analysis is the one we have described in the previous blog.

The exact mechanism is the following: we create two swaps, one with a maturity date on the last day of the month and one with a maturity on the first day of the month or shortly after. The first swap has a given notional (1 billion) and the second one has a notional slightly adapted to have the exact same total PV01 on the discounting curve.

The first example has a 6 month tenor and a fixed rate of 2.50% (not too far away from ATM). The swap is fixed semi-bond versus LIBOR-3M quarterly. The total PV01 for the discounting is by construction 0.00 USD. The total impact of the seasonality is 4.23 USD. From a pure PV01 comparison perspective, it seems that the change of discounting curve should not have any impact on the value but we still see some impact even if restricted. The bucketed PV01 is provided in Figure 1.

Figure 1. Bucketed PV01 of a short swap.

We could also have selected to have a total PV01 of 0 (not the discounting one equal to 0) or even all of them equal to 0 by adding small ATM swaps at each maturity. The results would not have been altered significantly.

In the second example, we look at a longer swap with a tenor of 2Y and a coupon of 10%. it represents the end of a long term swap that was traded some years ago when the rates were significantly higher than today. The maturities are 31-Jan-2021 and 5-Feb-2021. The bucketed PV01 is provided in Figure 2. Again the total PV01 for the discounting curve is 0. In this case the impact of seasonality is USD 1,842.38. Again that may look small but this is out of a PV01 of 0 for which the expected impact would have been close to 0.

Figure 2. Bucketed PV01 of a 2-year swap with a large fixed coupon.

We could have increased that impact by taking longer maturity swaps or focusing on end-of-year impacts. Note that the 1-Jan-2021 is a Friday and the end of year will be on a 4-day period. If we take a pair of zero-coupon swaps traded at the end of 2007/beginning of 2008 and ending one week apart around the end of 2020, we obtain a difference larger than USD 7,000. This was obtained with a end-of-month average spike of 13.5bps. If we were to use last year end-of-year spike which was above 60 bps for a couple of days, we would obtain impact larger than USD 30,000.

The amount above were obtain with a notional of 2 billions (1 billion in each direction). Given that the total outstanding amount at LCH is 150 trillions, the theoretical potential impact on valuation of the seasonality could be above 100 millions if the feature of dates of the second example was representative of the composition of the CCP book.

What is the impact of seasonal adjustment on your book? Do you have tools to incorporate the seasonality in your valuation mechanism and check if the proposed compensation for change of collateral/discounting is a fair compensation for your own book?

Don't hesitate to contact us to discuss how we can help in this process.

Fed Funds to SOFR: Impact of seasonality

The USD market is in transition between Effective Fed Fund Rates (EFFR) and Secured Overnight Financing Rate (SOFR) as the main overnight benchmark.

Once the transition will be completed, the main source of liquidity for OIS will be based on SOFR. For the OIS transition, the change will be gradual. The new OIS trades will be more and more linked to SOFR, but the legacy trade already entered into and linked to EFFR will not be directly affected.

Currently, the EFFR is not only used as the underlying for OIS but also, and maybe more importantly, used as the reference rate for the payment of interest on the Variation Margin (VM). The rate for VM is usually described in a CSA (non-cleared) or the house rule book (cleared). For the usage of the overnight benchmark in collateral, it is expected that the transition will be more "brutal". For example, LCH and CME have announced that they plan to switch from EFFR to SOFR at some stage in 2020. The switch will be done on one day, without gradual transition and without possibility for the members to switch from one to the other at their own pace.

The change of collateral rate impacts the present value of all the trades through the discounting. The exact details of the collateral discounting approach can be found in (Henrard 2014, Chapter 8). The collateral rate is part of the term-sheet of the trade (through the CSA or the rule book) and a change of term-sheet must be compensated in some way. To estimate the compensation, you need two ingredients: the difference of average between the two rates and the difference of "local behavior". In the case of EFFR v SOFR the difference of local behavior is the intra-month seasonality. As can be seen in Figure 1, the SOFR rate, based on a wider market, has some very clear seasonal behavior. In particular, one can see sharp rate increases at month-end that subside for a couple of days and some sharp increase around the 15th of the month, even if to a lesser extend.

Figure 1: Historical data comparison between EFFR and SOFR (most recent data missing due to issue with the Fed website).

In this blog we will look at the seasonal adjustment and how it can be incorporated in the curve calibration. In a forthcoming blog, we will look at the impact of the seasonality on the valuation.

The first step of this intra-month seasonality analysis is to quantify it. For this we used the historical data, which is now a little bit longer than one year, and estimated a couple of effects. We use a relatively simple method. We split the month is 6 parts: First business day of the month, second business of the month, the day starting on the first business day on or after the 15th, the second lasst business day of the month, the last business day of the month and the rest of the month. For each of this parts, we estimate the difference between EFFR and SOFR since the publication of SOFR. The results we obtained are provided in Table 1. One can see that the seasonal effect is significant with the month end reaching 13.5 bps above average, the peak subside over a couple of days (8 bps and then 4.5 bps) and a second, smaller, peak appear on the 15th of the month with a level of 4 bps. We have not found any specific impact on the second last day of the month. We do not claim that this is the best way to estimate the intra-month seasonality; each firm will have his own approach(es). We use those simplified number as an example of the impact on curve calibration

Description	Spread EFFR-SOFR (bps)	Adjusted to other	Adjusted to average
First	10.4	9.3	8.0
Second	7.0	5.9	4.6
15th	6.3	5.2	3.9
Second last	0.9	-0.2	-1.5
Last	15.9	14.8	13.5
Other	1.1	-	-1.3
Average	2.4	-	-

Table 1: Average of specific intra-month seasonality.

How to incorporate this information in the curve calibration? Obviously the curve after calibration should match the market exactly, so it is not a valid method to calibrate the curve with you favorite method and then to manipulate the result to incorporate those seasonality. After the manipulation, the curve would not match the market perfectly anymore. The seasonality has to be incorporated in the calibration step.

For the calibration presented here, we used OpenGamma's Strata library as the starting point. The library is very flexible in term of curve calibration and it is easy to extend and incorporate your own curve mechanism in it.

We have added a new type of curve. It consist of a "fixed curve", in which we incorporate the seasonality, and a variable main part. The two parts put together form a unique curve. We call the first curve fixed as we have created it from our historical data analysis and it will not be changed in the calibration procedure. The variable part is the one that will be calibrated.  Just to reiterate, we have one curve, which internally is divided in two parts, and we calibrate that one curve to the market. There will be no adjustment after the calibration. The one step calibration include both the general shape and the seasonal adjustment.

To match the usual shape of the overnight rate behavior, the main curve is interpolated using log-linear interpolation on the discount factors with node on the FOMC date. In that way the overnight forward rates follow a piecewise constant shape with jumps at the FOMC meeting dates (see Henrard 2014, Chapter 5 for the details).

We did the calibration described above with and without adjustment for seasonality. The calibration was done with market data from 21-Jun-2019. The non-adjusted curve is presented in Figure 2 and the adjusted one is added in Figure 3. Figure 4 depict the difference between the two.

Figure 2: Forward overnight rates implied by the curve calibration without adjustment to intra-month seasonality.

Figure 3: Forward overnight rates implied by the curve calibration with adjustment to intra-month seasonality.

Figure 4: Spread of forward overnight rates implied by the curve calibration with and without adjustment to intra-month seasonality.

In the difference one can see clearly the month-end and first days of the month impact and also the 15th of the month impact. Even if the above impacts have a fixed amplitude, the impact on the other part is not always the same. The reason is that the length of the months are different and in some cases, some of the dates above span a three calendar days period instead of one.

The code will be added to the muRisQ-ir-models open source library at a later stage.




Henrard, M. (2014). Interest Rate Modelling in the Multi-curve Framework: Foundations, Evolution and Implementation. Applied Quantitative Finance. Palgrave Macmillan. ISBN: 978-1-137-37465-3.

Is the LIBOR/SONIA spread curve flat?

In a recent blog we described the apparent convergence of the market basis spread to historical spot averages. This would be a consequence of the new fallback language based on historical mean/median. To illustrate this we have used USD 30Y EFFR/LIBOR basis swaps data and previously GBP 30Y SONIA/LIBOR basis swaps.

An argument that we have heard against our description of this convergence is that the spread curve is not flat. The argument is that if there was a convergence to historical mean, it should be the same for all tenors and the curve should be completely flat. If you look at the curve as of the end of May, you can see that the curve is not flat at all; the spreads are between 9 and 17 basis points. The graph of the GBP SONIA/LIBOR-3M basis spread for different tenors is displayed in Figure 1.

Figure 1: Shape of the GBP SONIA/LIBOR-3M basis spread curve as of 24 May 2019

Our answer is the following: The argument is correct but incorrectly applied. Yes, if the market has already incorporated the fallback on an average spread, the spread should be the same for all tenors and the curve should be very flat. But this argument applies only for swaps after the discontinuation date. The discontinuation is expected to take place at the start of 2022.

Now we can look at the same data with the correct glasses. What are the spreads for basis swaps starting somewhere after 2022 and with different tenors? We have not looked only at starts in 2022, but at forward starts with starting dates every 6 months for the next six years. The results are displayed in Figure 2.

Figure 2. Shape of the GBP SONIA/LIBOR-3M basis spread curve and several forward starting curves as of 24 May 2019

From that figure we can see two things. 1) the curve is (almost) flat for forward swaps starting after 2022. 2) The curves are not flat for swap starting in the next 18 months.

Not only is the market really pricing a flat curve in line with the convergence arguments but we can also infer that the market is not expecting a discontinuation in the next 18 months. The shape of the curve seems more an evidence for the convergence as described in previous blogs than against it.

Overnight benchmark collateral transition: delta impact

In USD and EUR, the main overnight benchmarks will be transitioning from a long serving benchmark to a relatively new benchmark.

In USD the current main benchmark is the Effective Federal Fund Rate (EFFR). The Secured Overnight Financing Rate (SOFR) which should replace it is published since April 2018. The transition to SOFR is relatively slow with only 0.2% of the notional traded in SOFR swaps with respect to LIBOR swaps year-to-date according to ISDA data.

In EUR, the current main benchmark is the EONIA. The Euro Short Term Rate (ESTER) which should replace it will be published from 2 October 2019. Due to the recalibration of the EONIA rate to ESTER plus a spread on the same date, it is expected that the EUR transition to the new benchmark will be a lot faster than the USD transition.

Once those new benchmarks are in place, one of the the most important change in the market will be to transition to that benchmark as reference rate for cash collateral. This is very important as the collateral rate is used in the valuation of all derivatives subjects to the Variation Margin (VM) in cash with the rate paid on the collateral referencing the benchmark. The details of the pricing mechanism in this context can be found in (Henrard 2014, Chapter 8).

Even if the main benchmark for collateral and the OIS market has switched to the new benchmark, there will still exists legacy trades referencing the old benchmark. Also we can expect that the most liquid market for the old benchmark will be based on overnight/overnight basis swaps.

If the market is moving in that direction, what will be the impact on delta risk of an OIS? We have tried to answer to that question with a simple example.

We used a USD 10Mx5Y OIS referencing EFFR. If we look at it in the current framework with EFFR collateral and with the most liquid market based in vanilla EFFR OIS, the risk is straightforward. It is displayed in Figure 1 below.

Figure 1: Delta for an OIS with cash variation margin and interest computed on the same benchmark as the OIS.

The main risk is between 5Y and 7Y at the maturity date and there is some risk between 9M and 12M at the effective date in the opposite direction.

If we look at the same trade in the expected new configuration, two things will change: the discounting will be done on SOFR and the most liquid market for EFFR will be based on basis swaps. The current standard for the SOFR/EFFR swaps is to quote the spread on the SOFR leg; this may change at some stage when SOFR becomes the standard. The delta risk in the new configuration is displayed in Figure 2.

Figure 2: Delta for an OIS with cash variation margin and interest computed on a different benchmark than the OIS. The market quotes the benchmark underlying the OIS through basis swaps.

The risk still appear on the same tenors. But now we see two risks. The SOFR risk and the basis risk. When a SOFR OIS rate increases and the spread is unchanged, EFFR rate increases through the basis swap. When the SOFR OIS rate is unchanged and the spread increases, EFFR increases also. This is why is seems that there is a duplication of the risk. The pure discounting (the coupon is not ATM) explain the small figures in the nodes 2 to 4 years. That risk appears only in the discounting and not in the forward. It is visible in Figure 1 in the EFFR column and in Figure 2 in the SOFR column.

The code that produced the above delta ladders can be found in the OvernightOvernightNodesCalibrationAnalysis class of the Analysis repository on Marc's Github repository.




Henrard, M. (2014). Interest Rate Modelling in the Multi-curve Framework: Foundations, Evolution and Implementation. Applied Quantitative Finance. Palgrave Macmillan. ISBN: 978-1-137-37465-3.

Mandatory IM: category 5

The mandatory bilateral Initial Margin for derivatives is approaching for financial institution in the Category 4 (aggregate month-end notional amount in March, April and May 2019 greater than EUR 0.75 trillion), with an implementation date of September 2019.

It is time for the institutions in Category 5 (aggregate month-end notional amount in March, April and May 2020 greater than EUR 8 billion) to prepare for the September 2020 deadline.

muRis_Q Advisory is specialized in interest rate derivatives. Our experience related to Initial Margin includes commenting on the regulatory consultations, implementing the first versions of ISDA SIMM and comparing CCP models to uncleared regulatory SIMM and ISDA SIMM. We have used the SIMM methodologies in many contexts. Our implementation for interest rate includes Algorithmic Differentiation features for efficient computation of IM differentiation (see our blog on Initial Margin and double AD).

On top of spot IM computation we have also worked on Margin Valuation Adjustments (MVA) from an academic and practitioner perspective. Some examples of our research can be found on our "Forward Initial Margin and multiple layers of AD" blog.

Don't hesitate to contact us for quantitative advisory on projects related to the mandatory uncleared IM framework, technical questions related to SIMM and associated MVA questions.

Fallback, historical spreads, and market convergence

Marc has been active on its personal blog trying to answer the question "Has the value transfer already started in the LIBOR fallback?". From the market data, it seems that the answer is yes. Once there is a value transfer, one can try to take advantage of it. Since November, he has published regular updates on the question, the most recent of them being Making money on LIBOR fallback (5).

We have developed a tool to systematically analyze this idea. In this blog we summarize its results for only one benchmark through a single graph. The benchmark is GBP-LIBOR-3M which could fallback to SONIA compounded setting in arrears. For that benchmark we looked at a total of 48 scenarios. Those scenarios where created using 8 announcement dates, 3 lookback periods (10Y, 7Y, 5Y) and the mean/median options.

The first item represented in the graph is the historical data of the market quoted spread on basis swaps GBP-LIBOR-3M v SONIA for a tenor of 30Y. We also represented the 48 scenarios. For each of them the running measure on each day over the last year has been computed. So each scenario has been run roughly 250 times to generate the curves.

This market has moved by roughly 5 basis points since the July 2018 consultation results announcement on 27 November 2018. The different scenarios still leave a range of 7 basis points for the fallback. The market is now at one of the bounds of the range that we have computed. This range should close when the exact methodology for the spread computation is published by ISDA.

On which side of the value transfer will you be on the next market move?

---

Related blogs:

0. Fallback transformers - Introduction
1. Fallback transformers - Present value and delta
2. Fallback transformers - Portfolio valuation
3. Fallback transformers - Forward discontinuation
4. Fallback transformers - Convexity adjustments
5. Fallback transformers - magnified view on risk
6. Fallback transformers - Risk transition
7. Fallback transformers - historical spread impact on value transfer

---

Don't fallback, step forward!

Contact us for our LIBOR fallback quant solutions.

Panel expert - Risk Live 2019

Marc Henrard has been invited as an expert panelist at the inaugural

Risk Live

organized by Risk.Net that will take place on June 2019 in London. The agenda of the conference can be found on the organizer web site:

Risk Live 2019 Agenda.

---

Marc will contribute to the panel

What could go wrong in Libor reform?

---

You can get a discount on the event with the speaker discount code below

Register from the link: https://bit.ly/2vm3lQe

---

Don't hesitate to reach out if you want to meet during the event.

Planning for the end of LIBOR - Cass Business School one-day workshop

Marc Henrard will present a seminar at the conference

Planning for the end of LIBOR

organized by Cass Business School in London on Wednesday 19 June 2019. The details of the workshop can be found on the organizer web site:

Cass Business School - Planning the end of LIBOR.

The event is free, but limited number of places are available. You have to register from the organizer's site referenced above. The registration is now open.

---

Marc's talk, will be titled LIBOR fallback: a quant perspective. It will be the opening session and will start at 10:00 am.

Abstract

With the increased expectation of some IBORs discontinuation and the increasing regulatory requirements related to benchmarks, a more robust fallback provision for benchmark-linked derivatives is becoming paramount for the interest rate market. Several options for such a fallback have been proposed and ISDA held a consultation on some of them. The results of the consultation has been to privilege the compounding setting in arrears and historical mean/median options. We present those options and emphasize their drawbacks. In particular the compounding setting in arrears lack of details and lack of measurability and they would make it not be achievable in practice. We also present an alternative option supported by different working groups. The historical option can lead to significant value transfer, some of them having already taken place.

---

Don't hesitate to reach out if you want to meet during the workshop.

LIBOR fallback: a recognised expertise

Over the coming years, one of the main issues in interest rate trading and risk management will be the emergence of new benchmarks and the potential IBORs fallback.

In the past year, we have looked at those issues from a theoretical and from a practical point of view. Some of the theoretical issues are detailed in a note that Marc published recently called "A Quant Perspective on IBOR Fallback Consultation Results" (https://ssrn.com/abstract=3226183). On the practical side we have implemented different fallback options, curve calibration mechanism and convexity adjustment to analyze the impacts on large portfolios. Some descriptions of the tools are available in a series of previous blogs.

Our expertise has been recognized by the market as documented from the invitations to many practitioner and academic finance conferences and seminars. Marc has been invited as guest speaker or expert panelist at the following events:

• The future of LIBOR (CFA Society Denmark, Copenhagen, Denmark) - 24 January 2019
• CASS Financial Engineering seminar (CASS Business School, London, UK) - 6 February 2019
• Quant Summit (organized by Risk.Net, London, UK) - 6-7 March 2019
• Singapore Management University seminar - 8 April 2019
• QuantMinds International (Vienna, Austria) - 14-16 May 2019
• CASS Business School workshop on LIBOR transition (London, UK) - 19 June 2019
• Risk Live (organized by Risk.Net, London, UK) - 27 June 2019
• The 15th Quantitative Finance Conference (organized by WBS, Italy, Rome) - 16 October 2019.
• The 5th Quant Insights Conference (organized by CQF Institute and Wilmott, London, UK) - 15 November 2019.

We are also presenting in-house workshops on similar subjects (see our training page on LIBOR) at different financial institutions in Europe.

Don't hesitate to contact us if you want to discuss potential in-house training or providing expertise on this subject for your projects.

Marc's presentation at QuantMinds International

Marc Henrard will present a seminar at the conference

QuantMinds International

which will take place from 14 to 16 May 2019 in Vienna. The agenda of the conference can be found on the organizer web site:

QuantMinds International 2019 Agenda.

See also Marc's page on QuantMinds site.

---

Marc's talk, will be titled A quant perspective on LIBOR fallback and will take place on 16 May at 9:50.

Talk's agenda:

• The current status of the fallback improvements 
• Potential difficulties with the proposed compounding in arrears option 
• Value transfer in the fallback 
• The RFR term rates

---

Don't hesitate to reach out if you want to meet during the summit.

Seminar at Singapore Management University

Marc Henrard will present a seminar at the

Singapore Management University

on Monday 8 April in Singapore. The details of the seminar and registration can be found on SMU website:

http://postgraduate.smu.edu.sg/acton/form/11522/025e:d-0003/0/-/-/-/-/index.htm

---

Marc's talk, will be titled A quant perspective on LIBOR fallback.

Talk's summary:

With the increased expectation of some IBORs discontinuation and the increasing regulatory requirements related to benchmarks, a more robust fallback provision for benchmark-linked derivatives is becoming paramount for the interest rate market. Several options for such a fallback have been proposed and ISDA held a consultation on some of them.

The results of the ISDA consultation has been to select the "compounding setting in arrears" adjusted rate and the "historical mean/median" spread approach. We analyse the proposed option in details and present an alternative option supported by different working groups. The presentation focuses is on the quantitative finance impacts for derivatives.

---

Don't hesitate to reach out if you want to meet at the seminar.

QuantCast on Risk.Net

New QuantCast on Risk.Net starring

Mercurio and Henrard on Libor transition and the need to involve quants early in discussions

Some of the elements of the discussion are based on an opinion published on SSRN: A Quant Opinion on LIBOR Fallback.

Marc Henrard in Risk.net's London studio
Photo: Iain Winfield

Risk.Net Podcast: LIBOR transition and fallback

Today Marc Henrard participated to a Risk.Net podcast related to LIBOR transition and fallback. The podcast will be published later this week on the publisher site. We will keep you posted about its publication.

IBOR transition and fallback trainings and workshops

In-house tailor-made training for all your team and your IBOR transition working group for the price of sending 2 of them to a standard training! The IBOR transition and fallback is a hot topic. Many course provider have jumped on the bandwagon. Those courses are provided at a premium price but with some speakers presenting for marketing purposes.

For the price of sending two staff members to those courses, you can have full in-house training from our experts that have analysed the subject for more than a year, participated to its consultations and done production-grade implementations. It is not a free lunch but certainly a relative value arbitrage opportunity! You invest less and you get more.

A typical agenda for such a course can be found on our training page. And as always, the course will be tailor-made to your specific requirements.

We are an (fiercely) independent management-owned advisory firm and our trainings reflect that independence. We don't have hidden agenda and are free of conflict of interest. All courses are backed by research and detailed in lecture notes provided to the participants. Part of the material of those trainings is used for a course in a master program in financial mathematics (Marc teaches a course on Interest rate modelling in the multi-curve and collateral framework at UCL).

Below is a graph representing the analysis of the USD-LIBOR-3M, SOFR and EFFR compounded. This is the type of analysis which forecast the almost 10 basis points in spread since 27 November 2018 (announcement date of the fallback methodology).

---

Don't fallback, step forward!

Contact us for our LIBOR fallback quant solutions.