Monday, 6 April 2020

Benchmarks in transition videos: Episode 3 - New ON benchmarks

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 derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The thrid episode describes the new overnight benchmarks in USD (SOFR) and EUR (ESTR).




All the videos will be linked in our LIBOR transition page.

Sunday, 5 April 2020

Benchmarks in transition videos: Episode 2 - Why?

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 derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The second episode is dedicated to the description of why a transition is required.




All the videos will be linked in our LIBOR transition page.

Saturday, 4 April 2020

Benchmarks in transition videos: Episode 1 - Introduction

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 derivatives is becoming paramount.

We have created a series of introductory videos on the subject of benchmark transition. The videos are available on our Youtube channel.

The first episode is dedicated to the description of Ibor and Overnight benchmarks.




All the videos will be linked in our LIBOR transition page.

Wednesday, 18 March 2020

LIBOR Fallback is not a curve change, its is a contract change!

In recent consultations, ISDA has proposed a new definitions for the LIBOR fallback. Similar definitions will probably be adopted by CCPs. The exact definitions have still to be clarified (LIBOR tenor or calculation period, calendar for 2 day shift, etc.), but the global idea is to replace a forward looking LIBOR by a backward looking composition on a different period. In previous notes and answers to the consultations, we have explain why the fallback cannot be applied exactly as described in the consultations, some new workaround will be required. Once those clear definitions are available and achievable, how do we include them in our pricing library?

The striking element of that change is not the change from one rate to another but the complete change of the LIBOR-linked derivatives term sheet. The term sheet is changed from a single rate known at the start of the period (or even 2 days before) to a combination of multiple rates known at (or around) the end of the period. This change of term sheet has a direct implication in terms of systems and valuation techniques. It is not possible to look at the fallback from a change of (forwarding) curve perspective. Yes a different curve will be needed, but this is only a very small issue. The main issue is that you have to dynamically change the instrument term sheet. By dynamically, we mean it is not a simple one-off re-booking of the trade in the systems. You may want to do the re-booking once the cessation has taken its full effects, by in the mean time you have to take the trade with its current description and do a what-if type analysis by changing the trade temporarily. The discontinuation date is still uncertain, so you need to do that transformation temporarily (in memory) and have the capacity to do it for several cessation dates, several spreads, several fallback definitions, etc.

This requirements is exactly why we developed the

almost 18 months ago.

We have seen some vendors proposing spread adjustment to RFR curves to price LIBOR swaps in the fallback. This is fine as a toy model to have an overview for vanilla swaps. But if you want a real in depth analysis, how does it work? How do you represent the 2 days shift effect, in particular when the 2 days cover a quarter-end, a year-end or a FOMC meeting? How do you include the difference between LIBOR tenor and calculation period? How do you include the jump on forward rate on the discontinuation date?

The decision to go the "transformer" route was not a random one for us. It was based on several prototypes in a production grade library and running detailed impacts on test portfolios with a market maker requirements in mind. Getting the general level correct by a shift is fine for a first global overview. The next step is to look at the details, at the pricing of short term instruments covering the transition expected date, at the impacts of date shifts, the exact curve shape at each intermediary date, etc. That can be done only by working on the instruments, not on the curves. Each instrument has its own idiosyncrasies that cannot be faked by a curve manipulation.

The inclusion of the jump on forward rate on the discontinuation date is particularly interesting for the moment. The current OIS/LIBOR spreads are very high with respect to the historical median. There is a real impact there. If you have a "fallback curve", how do you represent that? You could say that you would use a technique similar to the one you use for central bank meeting dates jumps. But unfortunately the impact is of a completely different nature. On the day before discontinuation, you have a forward looking LIBOR that covers 3 months. If you use a pseudo-discount factor approach to your LIBOR curve, you have a LIBOR curve for the next 3 months at the LIBOR level. For the 3 months RFR-based forward starting the next day, you need a RFR level (plus a fixed spread). But that RFR rate has an overlap of 3 months minus one day with the LIBOR. On that period, which rate do you use for the pseudo-discount factor curve? The LIBOR level or the RFR (+ spread) level? Today the UD-LIBOR-3M/OIS spread is around 75 bps while the historical median is about 25 bps. There is no way to get away from the contradiction between the levels with a curve approach. There is no reason to expect a convergence of LIBOR to RFR+spread as we appraoch the discontinuation date. And this is only for one single vanilla LIBOR payment, without even looking at the shift, period and composition issues. Even if the LIBOR had a fallback to a clean RFR term rate, this curve approach would not work at the transition.

We advice LIBOR-linked derivative users to implement the "trade transformer" approach in their internal libraries. Using curve based approach is running the risk of a nasty surprise when the actual cessation comes.


Figure 1: Historical time series of realized spread between USD-LIBOR-3M and SOFR compounded. The current crisis does not show yet fully on those figures as the SOFR compounded is backward looking. The full impact will be visible only in 3 months. For a forward looking view of the crisis impact, we refer to the previous post Forward looking the spread between forward looking and backward looking rates.

Figure 2: Distribution of realized spread between USD-LIBOR-3M and SOFR compounded with teh current median. The most recent realizations are in lighter colours. The most recent ones are mainly above the current median and we can expect that the median will increase in the coming months. More details are available in the previous post LIBOR Fallback: a median in a crisis.



We have done many other developments around the analysis of valuation and data in the context of the LIBOR fallback. This includes analysis of value transfer impacts, forward spreads, minimum and maximum spreads, discounting big bang, estimations based on forward curves with calibration using spread control (see Curve calibration and LIBOR-OIS spread).

Don't hesitate to reach out to discuss how those developments could be of interest in the context of the management of your portfolio.

Saturday, 14 March 2020

LIBOR Fallback: a median in a crisis

The ISDA proposed LIBOR fallback mechanism is based on a 5-year historical median estimate. If the LIBOR discontinuation take place as expected in January 2022, we already have a certain portion of the required historical data.

In this analysis, to keep the number of variables low, we look only at USD-LIBOR-3M and suppose that the announcement date is 1 September 2021 (3 month before January 2022). We interpret the "5 year of history" as meaning 5 years of LIBOR fixing for which we have the relevant SOFR fixings. This means we actually use 5 years and 3 months of overnight data (other interpretation of "5 years history" are possible). The LIBOR fixing are from 29 June 2016 to 29 June 2021.

We can plot the historical data from the known period (29 June 2016 to 13 March 2020); the histogram of the data is provided below. The figure also displays the median (as per ISDA proposal) and the median (for comparison). The median is 26.6 bps and the mean 29.2 bps.


There is still the period from 16 March 2020 to 29 June 2021 which is unknown. The proposal is to use the median. We have 876 data points out of the 1260 required. We can already put a hard bound on the lowest and highest possible median spread (conditional to our date hypothesis). The lowest median possible is 20.2 bps and the highest median possible is 36.5 bps. Those figures are represented below.


What about the mean? The mean depends on the exact value of each number, and there is no a priori bound on the individual spreads, so no a priori bound on the mean either. We can nevertheless create some "what-if" analysis. For that we use two extreme scenarios: one with all the remaining spreads at 0 bps and one with all the remaining spread at 100 bps. The graph of those values is proposed below.


The different daily spreads are not independent. There is significant overlap between the overnight rates used in consecutive daily spreads. The spreads tend to cluster, creating a trend in the median evolution. Where are we today (or more exactly were are we in the combination of LIBOR from 3 months ago and overnight up to today)? In the figure below, the have colour-coded the different occurrences. The lighter colours represent the more recent ones, each colour representing one of the 8 groups of 10 prints (a total of 80 recent print are in lighter colours).


The trend in the last months has been to be higher that the median. Note that the above figure do not include the LIBOR rates from the recent turbulent weeks; those will appear in the statistics only in a couple of months. Our best predication of those (see our recent post on Forward looking the spread between forward looking and backward looking rates) is that there will soon be very high spreads (above 100 bps).

This lead us to an embedded option in the fallback proposal. We mention our best estimate of the spreads in the coming months. Suppose that our estimation is perfect, are we sure that those spread will be included in the actual spread computation? The computation of the spread will be done on the announcement date (not on the cessation date). The announcement date will be decided by IBA and the panel banks, the procedure is thus giving a (free) option to the panel banks. Even disregarding the potential material nonpublic information embedded in the decision, there is a real option of non negligible value. Suppose that the option is exercised today and the announcement is made today (for an actual cessation in January 2022), what would be the impact? It is graphically depicted in the figure below. The direct impact would be an estimated margin of 24.5 bps, which is a decrease of 2 bps with respect to the first estimate in this post. Maybe more importantly it also removes the possibility of the spread going up to 36.5 bps which would be the case if all (market) spreads in the next 2 years or so were to be above 36.5 bps. The announcement option has a potential value of as much as 12 bps on all transactions with fixings post January 2022.


What are your options with regards to the fallback and how do you plan to exercise them? Don't hesitate to contact us to estimate them.



We have done many other developments around the analysis of spread data in the context of the LIBOR fallback. This includes analysis of value transfer impacts, forward spreads, minimum and maximum spreads, estimations based on forward curves with calibration using spread control (see Curve calibration and LIBOR-OIS spread).

Don't hesitate to reach out to discuss how those developments could be of interest in the context of the management of your portfolio.

Thursday, 12 March 2020

Forward looking the spread between forward looking and backward looking rates

Forward looking the spread between forward looking and backward looking rates or estimating the market misestimation 

The planned approach to adjustment spread in the new derivative LIBOR fallback arrangements are based on historical data. The spread historical data is based on one side the LIBOR forward looking rates and on the other side on the backward looking compounding setting in arrears.

This arrangement creates a spread which is a mixture of credit spread and market misestimation (see A Quant Perspective on IBOR Fallback consultation results, Section 5.2 for previous remarks on this). What is happening to that spread with the current crisis? By definition of the spread itself, we will be able to analyse this only in 3 months time, when all the overnight rates prints are known and we can compare the then backward looking overnight rate to the today forward looking LIBOR rate.

But it is possible to do a little bit better. We know the LIBOR rates over the last 3 months and we can project the overnight rates for the next 3 months. That does not really help us for the spread corresponding to today fixing, but it will help for the LIBOR fixing over the past three months. It is possible to get an estimate of the surprise (surprise cut in this case) that has already been realised.

The following graph is the result of that exercise for USD-LIBOR-3M and USD-SOFR. The LIBOR rates (dark blue line) are know up to today. The SOFR compounding rate in arrears based on the actual fixing (light gray line) are known up to the period corresponding to the fixing from 3 months ago. The projected in arrears for the 3 months up to today (dark grey) are based on known fixing up to today and projected fixing up to the end of the 3-month period. The spreads up to 3 months ago (yellow) are fully known and the spreads up to today are partly known (red) with the LIBOR side fully known and the SOFR side partly known.

We can see that the (projected) data already includes spike in the spread due to the surprise cut. The spike is above 100 bps. On the other side, for the fully forward looking LIBOR versus the fully forward looking SOFR (last red point on the graph), this is a spread without any unexpected element of monetary policy, has a spread larger than the average/median over the last years but is very far away from the spike. It does not mean that the credit crisis is suddenly seen as less severe over the last days, only that the market is not expecting unexpected policy changes.





We have done many other developments around the analysis of spread data in the context of the LIBOR fallback. This includes analysis of minimum and maximum spreads, estimations based on forward curves with calibration using spread control (see Curve calibration and LIBOR-OIS spread).

Don't hesitate to reach out to discuss how those developments could be of interest in the context of your portfolio management.

Sunday, 8 March 2020

Signing the LIBOR fallback protocol: a cautionary tale (2)

Following recent market moves, the graph accompanying the cautionary tale published in Risk.Net has been updated.

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


Updated without comment!

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: https://ssrn.com/abstract=3530464.



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  http://ssrn.com/abstract=3520619.

Conclusion:

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 http://multi-curve-framework.blogspot.com/2018/10/isda-consultation-on-libor-fallback-my.html.

LIBOR Fallback transformers! 
Market Infrastructure blog, muRisQ Advisory, October 2018.
Available at https://murisq.blogspot.com/2018/10/libor-fallback-transformers.html.

A Quant Perspective on IBOR Fallback consultation results.
Market infrastructure analysis, muRisQ Advisory, January 2019.
Available at http://ssrn.com/abstract=3308766.

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.

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.

LIBOR fallback and quantitative finance. Risks, 7(88), August 2019. Open Access article available at https://doi.org/10.3390/risks7030088.

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 https://informaconnect.com/quantminds-international/ibor-workshop/

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: https://github.com/marc-henrard/analysis).

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.