Sunday, 2 February 2020

Discounting transition: big bang impacts

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.

CCPs are planning a big bang-like collateral and discounting transition for USD. In theory this transition is done with value compensation and risk exchange at fair market value. Such a transition would conduce to the absence of value and risk impact. But by definition of big bang, the transition is done in an illiquid market for which the fair theoretical value is unknown.  To understand the actual impact on valuation and risk, one has to look at the practical details of the transition and how the absence of data for half of the required theoretical quantities is overcome in practice. The resulting situation prompts exotic convexity adjustments for cleared swap and unknown valuation for non-cleared products.

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

Discounting transition: big bang impacts

and is available on SSRN with the reference

Henrard, Marc P. A., Discounting transition: big bang impacts. Market Infrastructure Analysis, muRisQ Advisory, February 2020. Available at SSRN:

Other post related to the discounting transition: Change in collateral rate at CCP: quant perspective.

Tuesday, 21 January 2020

Signing the LIBOR fallback protocol: a cautionary tale

As Orwell's Room 101 beckons for LIBOR publication, muRisQ Advisory's Marc Henrard warns of potential pitfall in the fallback protocol.

This is the Risk.Net introduction to Marc's comment about the cleared/uncleared fragmentation of the market due to the design of the IBOR fallback.

The full text is available on Risk.Net website (subscription required):

Figure from the above published comment.

Note that the issue of the market fragmentation will be particularly visible in EUR where it is expected that EUR-LIBOR will be discontinued at the end of 2021 and EUR-EURIBOR will continue to exist probably for a further 5 years. It appears that the EUR-LIBOR fallback will be done directly to ESTR and not to EUR-EURIBOR as suggested in our answer to the ISDA EUR fallback consultation. Any payment originating from LIBOR fallback will be easy to compare to an actual EUR-EURIBOR payment (see also the post about the EUR curve shape not in line with ISDA fallback at all).

The discrepancy between fallback contaminated and clean versions of LIBOR payments should be taken into account in bond reference rate switch from LIBOR to SONIA. A popular method seems to infer the adjustment spread for bonds from the swap market as reported in Nationwide and Lloyds win nod for Sonia bond switch (subscription required). But those spreads are based on the historical past spread, not on the forecast of actual LIBOR-like value. Obviously the switches have been done with the approval of the note-holder, but was that approval based on a clear understanding by the note-holders of what was behind those contaminated cleared swap market figures?

Saturday, 18 January 2020

Answer to ISDA consultation on EUR-LIBOR and EUR-EURIBOR fallback

ISDA consultation regarding EUR-LIBOR and EURIBOR fallback closes in a couple of days. As for the previous consultation, we have provided a detailed answer. The text of our answer can be found on SSRN: Answer to ``Supplemental Consultation on Spread and Term Adjustments, including Final Parameters thereof, for Fallbacks in Derivatives Referencing EUR LIBOR and EURIBOR, as well as other less widely used IBORs'' issued by ISDA


The consultation is based on question similar to the previous consultations. The answers we provided to those consultation and the quantitative literature related to the same subject can be used to understand why the proposed solutions are not acceptable.

To those generic answer, there are two EUR specific issues that should be emphasised. The first one is positive and is the existence of two benchmarks (EUR-LIBOR and EUR-EURIBOR) with one of them expected to outlast the other by several years. The surviving benchmark should be used as the first step of the fallback for the other benchmark. The second issue is negative and is due to the fact that the planned fallback benchmark, ESTR, has been published only since 1 October 2019. Data preceding that date are for some part not intended for use as benchmark by the administrator and regulator and for the older part not regulation compliant. The only ESTR data acceptable is the one officially published as a benchmark, i.e. data for dates after 1 October 2019.

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

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

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

LIBOR Fallback transformers! 
Market Infrastructure blog, muRisQ Advisory, October 2018.
Available at

A Quant Perspective on IBOR Fallback consultation results.
Market infrastructure analysis, muRisQ Advisory, January 2019.
Available at

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

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

LIBOR fallback and quantitative finance. Risks, 7(88), August 2019. Open Access article available at

LIBOR: Don't fallback, step forward. Wilmott Magazine, November 2019.

Fallback protocol signature: a cautionary tale. Risk.Net, January 2020, to appear.

The figure is extracted from the post related to the "EURIBOR: The market does not believe in ISDA fallback in the next 10 years!"

Figure 3: Time series of EURIBOR and (pre-)ESTR compounded with 6-month underlying period.

Thursday, 16 January 2020

Marc's workshop at QuantMinds International 2020

Marc Henrard will present a workshop and a seminar at

QuantMinds International

which will take place from Monday 11 May to Friday 15 May 2020 in Hamburg. The agenda of the conference can be found on the organizer web site:

Marc's workshop, will take place on Friday 15 May and will be titled Benchmarks in transition: Quantitative perspective on benchmarks, transition, fallback and regulation..

The workshop agenda can be found on the organizer website at

The workshop can also be run as an in-house course tailor made to your needs as described on our training page related to benchmarks.

We will add the details of the talk closer to the date. 

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

Saturday, 11 January 2020

Marc's presentation at the Quant Summit Europe 2020

Marc Henrard will present a seminar at the

Quant Summit Europe

which will take place on Wednesday 11 and Thursday 12 March 2020 in London. The agenda of the conference can be found on the organizer web site:

Marc's talk, will be titled LIBOR fallback: the cost of a signature.

Talk's agenda:
  • ISDA fallback methodology 
  • Value transfer in the fallback 
  • ISDA protocol signature crystallize the value transfer: what is its cost?

As a speaker at the summit, we can offer our guests a 20% discount. Contact us for the discount code.

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

EURIBOR: The market does not believe in ISDA fallback in the next 10 years!

ISDA has launched a couple of weeks ago a new consultation related to IBOR fallback. This consultation is related to EUR-LIBOR and EUR-EURIBOR (and undisclosed other IBORs!). In the previous blogs about the fallback over the last 2 years, we have not provided any figure for EUR. The reason was two fold: we don't really believe in imminent EURIBOR fallback and the EUR rate market has been completely dormant for several years and it is very difficult to read anything in that market.

With the questions about the EUR fallback coming to the fore, it is a good time to try to read something from the market rates.

The conclusion is the title of this post:
The market does not believe in ISDA proposed fallback for EURIBOR in the next 10 years!

The conclusion is intentionally ambiguous. It can be read that the market does not believe that the ISDA proposed fallback methodology will be adopted in the next 10 years or that there will be no requirement for a fallback in the next 10 years, i.e. that EURIBOR will survive that period.

Before explaining the conclusion, we need to describe the data and the premises of the analysis. The data is based on historical ESTR (and pre-ESTR) figures, historical EURIBOR and current basis spread market.

The ESTR benchmark was officially started on 1 October 2019, but ECB has published pre-ESTR figure with values dating back to 15 March 2017. If we include the pre-ESTR figures in the analysis that is almost 3 years of data. Without the pre-ESTR data, there is a little bit more than 3 month of data, this is not enough to compute one single ESTR compounded in arrears for one 6-month period! The pre-ESTR figures are, according to the ECB, not intended for use as a benchmark in any market transaction, whether directly or indirectly", but are acceptable for personal analysis.

With the ESTR data, I have computed the composition on EURIBOR periods 1, 3 and 6 months. The computation is done using the open source code that I have posted in February 2018. The ESTR compounded rates are then compared to EURIBOR and median is computed (using code posted in Marc's Analysis repository:

The historical time series of ESTR compounded are represented graphically in the figures below. The full data is also available in the analysis repository described above.

Figure 1: Time series of EURIBOR and (pre-)ESTR compounded with 1-month underlying period.

Figure 2: Time series of EURIBOR and (pre-)ESTR compounded with 3-month underlying period.

Figure 3: Time series of EURIBOR and (pre-)ESTR compounded with 6-month underlying period.

As can be seen in the data, there was very little volatility in ESTR and in EURIBOR and consequently very little volatility in the relevant spreads.

Let's look at the 1-month, 3-month and 6-month tenor spreads against ESTR compounded in arrears. The medians are 7.95 bps, 12.41 bps and 18.06 bps. Those medians are the relevant figures for the ISDA fallback methodology. Those spreads imply a 6-month/3-month basis spread of 5.65 bps.

What is the market saying? Looking at the 10-year tenor basis swaps, we see a spread of around 6.20/6.50 bps. That seems roughly in line with the above computed spread. Two possible explanations for that figure: the market believe in the imminent fallback of EURIBOR to ESTR using ISDA proposed methodology for the spread or this is a coincidence. To decide between the two, let's look a the spread curve shape. If EURIBOR fallback to ESTR + spread in the next 10 years, the fallback being definitive, it will still be there in the 20 following years. What is the 30-year tenor basis spread? The spread is just below 3 bps. A back of an envelop computation give a spread of around 1.25 bps for the 20 years between 10 and 30 years. Definitively the market does not indicate an expectation of the ISDA proposed fallback to apply to EURIBOR in that period.

Maybe we are missing something in the computation. The market may expect the spread implied by the realized LIBOR/ESTR fixings to decline to a small figure in line with the long term quoted spread. But the spread for the 10-year tenor basis swap is around 6.5 bps, the market expect that spread to be realised, so it expect that the spread on the ISDA proposed 5-year look-back spread will be around that figure.

We are oversimplifying the story in the above paragraph. The market 6.5 bps is an average in the risk neutral measure but the historical spread is a median in the historical measure. Can the difference between the two explain the difference? If yes, would it make sense to try to statistically arbitrage this difference?

Another issue is that the ISDA proposed spread is based on realised spreads between forward-looking LIBOR and realized backward-looking compounded ESTR. The spreads contain the credit and liquidity spreads but also the misestimation by the market of the forward looking rates with respect to the backward looking ones. The market may have an estimation of the market misestimation that explain that difference (!).

We are digging quite deep to try to find an explanation. Even if the above explanations are theoretically possible, they seem far fetched. The best explanation seems that
The market does not believe in ISDA proposed fallback for EURIBOR in the next 10 years!

Is it the expectation of a different fallback or the expectation of the EURIBOR to survive for another 10 year? We don't know. We expect EURIBOR to survive at least to 2027 (2022 + 5 year) if a clean transition (including a clean fallback) is not developed in the mean time.

Note: Other long term spreads do not match our computed median spreads:
1Mv3M: historical 4.46 bps - 30Y basis swap 2.3/2.9 bps
ESTRv3M: historical 12.41 bps - 30Y basis swap 8.5/9.1 bps

Maybe there is a way to make money on EURIBOR fallback.

Saturday, 14 December 2019

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.

Tuesday, 19 November 2019

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.


  • 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)


  • 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)


  • 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

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

Monday, 18 November 2019

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: and the difference in volatility between LIBOR and OIS (Hybrid Model: A Dynamic Multi-Curve Framework, August 2018. Available at SSRN:

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 monthOTC startED endOTC endED lengthSOFR lengthOTC 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

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