Sunday, 27 December 2020

New publication: Description of overnight floaters with principal adjustment and its advantages

A new working paper related to fallback and composition for bond has been made available on SSRN. The paper title is

Description of overnight floaters with principal adjustment and its advantages.

The paper is available on SSRN at

Abstract

Interest rate markets are moving away from term benchmarks to embrace overnight benchmarks more widely. This has created an issue for bonds and loan markets as direct application of the overnight standard mechanism, the composition, leads to coupons that are known only at the end of the accrual period. We provide a precise description of a less known convention for those products which has the same level of complexity that the direct method but has the important advantage to lead to coupons that are known at the start of the accrual period for all but the last coupon. This simple convention is apparently misunderstood, including in official regulatory documents, and it appears that a systematic description and formal analysis of its valuation and risk mechanism would be beneficiary for the market.

Wednesday, 23 December 2020

Historical spread adjustments: USD figures

We compute estimates of the historical spread adjustment for USD-LIBOR on a regular basis. The data below is as of 2020-12-22.

Spread type USD-LIBOR-1M USD-LIBOR-3M USD-LIBOR-6M
Current Median 11.8796 26.9280 45.5777
Minimum Median 11.6466 26.2982 42.8282
Maximum Median 12.2351 28.1811 49.1824
Mean 13.9231 33.6027 50.9622
Mean-Median 2.0435 6.6747 5.3845

Contact us for more details on the hypothesis and methodology used.

We can provide production grade code that run those estimates on a daily basis.

Figure: Distribution of USD-LIBOR-1M / USD-SOFR compounded in arrears over 1M.

Tuesday, 22 December 2020

The Université de Paris Libor transition workshop

Marc Henrard will be a keynote speaker and panelist at the

Libor transition workshop

oranized by The Université de Paris. The workshop will take place online on Thursday 21 January 2021 at 18h00 (Paris time). The attendance is free. The details of the workshop can be found on the organizer website:

Added 2021-01-05: An earlier version of the post indicated the presentation would take place on 11 January. The date has now be move by 10 days.

Tuesday, 15 December 2020

Marc quoted in the press: Practice Insight - IFLR

Marc was quoted in the press in an article related to the EONIA/ESTR transition: Authorities renew calls for €STR take-up (subscription required).

The quotes are

Since the publication of ISDA's supplement 60 to the ISDA 2006 definitions, all new Eonia trades have a robust fallback – therefore the lack of adequate fallbacks isn’t an argument for new trades, and switching old contracts won’t help the take-up for new ones,” said Marc Henrard, managing partner at muRisQ Advisory.

“What concerns me, however, is the ability for systems to handle the Eonia fallback. I would strongly encourage people to move to €STR, but I expect Eonia curves to stay in banks’ systems for several years – even after January 2022." "Admitting that systems cannot cope with the fallback is, in my sense, a stronger argument than the others for switching to the RFR,” he added.
and
The ECB also said it considered publishing compounded term rates based on €STR as well as a daily index to encourage a wider adoption of the rate. “I don’t see how this would be used in practice, except for some retail products,” said Henrard. “From a daily perspective for financial institutions, I don’t see how it would fit in. It would certainly generate problems as opposed to solving them. If there was any use to this, it would have probably been implemented for Eonia 20 years ago.”

Sunday, 6 December 2020

Description of ON floater with hybrid rate payments and its advantages

Description

In this section we provide more details about the hybrid approach to the term sheet of bonds and loans. This is based on compounding in-arrears mechanism but with improvements that make them easier to deal with, specially in relation to the forecast of cashflows at the beginning of each period. This approach has been previously described in a December 2019 blog : Compounded rate out of favour: what now? (2).This type of approach may have been described before, but the author is not aware of any related literature.

At start of each period, a fixed rate is decided for the period. This rate is not a definitive rate, but an advance on interest rate. At the end of the period the standard compounded in-arrears rate is computed. The difference between the compounded rate and the advance is added to the notional to be repaid.

The way the rate fixed at the start of the period is not very important. Its impact on valuation or risk management is minor; it is of the same order of magnitude that a spread above compounded rate.

Set of payment related date: ti (i=0,..., n). t0 the start date and ti (i>0) the actual payment date. Each of the periods [ti-1,ti] (i=1,..., n) is divided in overnight periods (ti,j) (j=0,..., ni) with ti,0 = ti-1 and ti, ni = ti.

For a period notional Ni, the compounded interest amount is


The interest rate paid on the end of period i is Ri. The rate Ri is Fti-1-measurable, i.e. it is decided at (or before) the period start. After that period, the notional is adapted with


The total cashflow equivalent in ti is this the interest paid plus the notional increase. This is equal to


At the end of the last period, the amount repaid is notional plus interest, i.e.

Whatever the choice for Ri is done, in all cases, the periodic payment at each coupon date is equivalent to a compounded rate. The final payment include notional plus compounded interest. The notional is slightly change at each period but that does not bring any complexity as the rate is the fair rate for the period. It is not more complex than a loan/bond with variable notional paying floating fair coupon.

The valuation and risk analysis above is valid whatever the rate Ri is selected. It can be some last reset ``in-advance'' composition, last recent or even a random number. For operational purposes, it is enough that it is selected at the start of the period and for valuation/risk purposes, it is enough that it is consider as an advance on interest due with the difference embedded in the notional and not a final interest amount.

Advantages

In a recent consultation paper from the ECB, the feature of this approach has been incorrectly described as creating significant operational complexity, with more complex and less transparent calculation and relevant hedging issues expected. Based on the description provided above, it is clear that those element are inaccurate. As the paper does not provide any reference to relevant literature or explanation about the reason of those characteristics, we believe that further analysis of those issues are warranted.

One of the issues with compounded in-arrears mechanisms is that the payment has to take place on the same day that the final amount is known. This mechanism is not different from other in-arrears in that respect. In this context, the obvious advantage of the hybrid approach is that the issue appears only once, on the very last payment. The same range of solution discussed for the in-arrears can be used in this case also. This is a different discussion that is not debated here. Without doubt, the issues is easier in this case as it is relevant only on the last payment instead at each payment.

Operational ease/cash flow management

As mentioned above the operational ease and cash flow management issues are better in this mechanism. All cash flows, except the last are know at the period start.

Computational ease/mechanics

The only small issues is the new notional computation. Computing the coupon for in-arrears on a 3 month coupon (60 business days) take approximately 120 multiplications and 60 additions. The notional computation in the hybrid case requires one extra multiplication and one extra addition. If the usual (credit/profit) spread is added to the picture, as the rate fixed in advance plays the same theoretical role as the spread, the extra complexity is only one addition.

Hedging ease

In term of hedging, the notion of hedging ease or complexity is obviously relative to what is the target risk. Here we suppose that the target is to have not market risk and that the composition of overnight rates is considered risk free. In that case, most of the risk is on the composition and does not need any hedging. The only difference is that the notional is slightly changing at each period. The rate fixed at each period does not need any hedging, it is used as a repayment of part of the notional at each step. The addition of a spread may require a hedging in the same way as the addition of a spread may require a hedging with pure in-arrears coupons.

The credit risk of such a bond is not significantly different to the one of other bonds. No specific changes are required.

Usage and client acceptance

This type of bond/loan is not used currently. The acceptance by clients is unknown. The consultation paper mentioned above indicates that such mechanism are not observed. It indicates, without explanation, that the client acceptance is potentially low. As long as the adverb potentially is used, this is true. It would as true to say that the client acceptance is potentially very high.

Advances on final bills are a standard concept in retail and services. There is no reason that such a simple and widely used concept would not be accepted by sophisticated participants in the financial markets.

Next step

We have contacted the ECB/Working group to require a correction of the consultation paper.

A preprint version of this text will be made available on a preprint server soon. The link will be added.


Note added 2021-01-02: We have not yet received any answer from the ECB/Working group.

The new working paper related to the principal adjustment method for bonds and loans as been made available on SSRN:

Description of overnight floaters with principal adjustment and its advantages.

The paper is available on SSRN at

Thursday, 5 November 2020

Marc's presentation at QuantMinds International

Yesterday's presentation at

QuantMinds International

is now available on demand on the conference website (Wednesday 4th, Stream C). 

The presentation was based on proprietary research that has been published in Risk.Net: CCP discounting big bang: convexity adjustment.

A couple of screen shots:





Tuesday, 20 October 2020

Marc's presentation at QuantMinds International

 Marc Henrard will present a seminar at 

QuantMinds International


which will take place from Monday 2 November to Friday 6 November 2020. The agenda of the conference can be found on the organizer web site:




Marc's talk will take place on Wednesday 4 November at 9h00 am and will be titled CCP Discounting Big-Bang: The irony in the derivatives forwarding.

Agenda:

  • Collateral and discounting big-bang process
  • Valuation impacts: theoretical clean process
  • Valuation impacts: practical dirty process
  • Convexity adjustments: forwarding big bang


The proprietary research underlying the presentation is detailed in a paper that has been published in Risk.Net: CCP discounting big bang: convexity adjustment.

Wednesday, 23 September 2020

Published: CCP discounting big bang: convexity adjustment

 A new timely research paper developed by Marc has been published in Risk.Net. The paper is titled

CCP discounting big bang: convexity adjustment



The CCP discounting big bang in USD is planned to take place in mid-October. The paper has been published on 18 September 2020 and is available at (subscription required): https://www.risk.net/cutting-edge/banking/7682566/ccp-discounting-big-bang-convexity-adjustment

Introduction:

Central counterparties are planning big bang-like collateral transitions. The transitions are done in an illiquid market and some fair market values are unknown. The CCP-selected mechanism to deal with these unknowns gives rise to exotic convexity adjustments. In this paper, Marc Henrard analyses the origin of those adjustments and quantifies the resulting impact based on a model for the dynamics of the relevant discounting and forwarding rates

Wednesday, 26 August 2020

Marc quoted in the press: Practice Insight - IFLR

Marc was quoted in the press in a follow-up article to the "Where is ESTR?" article previously reported. This article, dated 26-Aug-2020, was titled Market still reluctant to adopt €STR (subscription required).

Tuesday, 18 August 2020

New paper: CCP discounting big bang: convexity adjustment

A new timely research paper developed by Marc has been accepted for publication in Risk.Net. The paper is titled

CCP discounting big bang: convexity adjustment


The CCP discounting big bang in USD is planned to take place in mid-october.

Abstract: 

CCPs are planning a big bang-like collateral and discounting transition for USD. This transition is described as providing value and risk exchange compensation at fair market values. Such a transition would conduce to the absence of value and risk impact for market participants if it was done in a pure way. By definition of big bang, the transition is done in an illiquid market for some market segments and some fair market values are unknown. To understand the actual impacts, one has to look at the practical details and how the absence of data for half of the values is overcome in practice. The CCP selected mechanism prompts exotic convexity adjustments for transitioned swaps. In this note we prove that a clean approach would really be clean and analyse the details of the practical approach and its adjustments for vanilla swaps.

Part of the research has been presented at the Online Interest Rate Reform Conference in July 2020 under the title "CCP discounting big bang: The Irony in the derivatives forwarding".


Note added 2020-08-20: The publication is planned for the October paper issue of Risk.Net. It should appear in the online version earlier. A link to the paper will be posted when available online.

Note added 2020-09-23: The link to the online paper is (subscription required):  https://www.risk.net/cutting-edge/banking/7682566/ccp-discounting-big-bang-convexity-adjustment

Tuesday, 28 July 2020

muRisQ in the press: SOFR related data in Risk.Net

The (difficult) transition to SOFR continues. According to the different press reports, the take-over is slower than expected and in some niche market, LIBOR-linked FRNs are growing faster to SOFR-linked ones. Some of those isses are discussed in a recent Risk.Net article: Asia debt market suffers SOFR inertia.

Even if Bloomberg has started to publish SOFR compounded data, the specialized press still relies on data computed and provided by muRisQ Advisory. The preference to muRisQ data is visible in the Figure 4 of the above mentioned article.


All the graphs and figures in our blogs, seminars and videos are produced by production grade libraries. Our libraries include the Fallback Transformers which allow to apply the exact fallback details to actual trades and portfolios. The transformation details include overnight composition, period offset, spread applicable, and discontinuation date. They are suitable for what-if analysis and risk management.



Don't fallback, step forward!

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

Sunday, 5 July 2020

Marc quoted in the press: Practice Insight - IFLR

LIBOR transition is certainly of great interest to the quant side of the financial industry, as illustrated by numerous seminars over the last years (see here for a list to which we contributed) but also numerous columns, interviews, and quotes from Marc in Risk (eg Signing the LIBOR fallback protocol: a cautionary tale, Pandemic and LIBOR, LIBOR transition mismatch fear, muRisQ quoted in ISDA consultation summary).

The transition has also an impact on the legal side of the financial profession. A recent slightly provocative blog by Marc (Where is ESTR?) has been the starting point of an article in Practice Insight - IFLR titled "Euro risk-free rate: where is €STR?". Practice Insight is a "news service for lawyers, tracking how financial institutions are implementing Europe's capital market rules" (subscription required).

Wednesday, 10 June 2020

Benchmarks in transition videos: Season 1: all the episodes


We have created a set of introductory videos related to Benchmarks in transition. There is a total of nine videos which are available on our Youtube channel
  1. Benchmarks: tenor deposit and overnight (11:32)
  2. Why a transition? (15:01)
  3. Overnight transition: EFFR to SOFR and EONIA to ESTR (21:10)
  4. CCP big bang - EUR (6:32)
  5. CCP big bang - USD (21:42)
  6. IBOR fallback - overview (16:40)
  7. IBOR fallback - adjusted RFR (18:06)
  8. IBOR fallback - spread (17:11)
  9. IBOR fallback - value transfer (17:34)
The videos are at the introductory level for each subject. A lot more material is available for workshops and advisory engagements. The slides of the videos are available at: http://ssrn.com/abstract=3568503.



All the graphs in our blogs, seminars and videos are produced by production grade libraries. Our libraries include the Fallback Transformers which allow to apply the exact fallback details to actual trades and portfolios. The transformation details include overnight composition, period offset, spread applicable, and discontinuation date. They are suitable for what-if analysis and risk management.



Don't fallback, step forward!

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

Sunday, 31 May 2020

Fallback transformers: gaps and overlaps - portfolio version

In a previous blog, titled Fallback transformers: gaps and overlaps we have described the (unintended?) consequences of the offset mechanism in the IBOR fallback computation period described in the Bloomberg IBOR Fallback Rate Adjustments Rule Book.

From the fallback rule book, does it transpire what the graph below represents? If not, continue reading!


Figure 0. Overnight weights to be explained.

The proposal for the period is to offset the overnight compounding period start with respect to the IBOR period start by two (business) days and to compute the overnight compounding period end as the IBOR tenor after the start (in the modified following convention). As very well known by practitioners, the period additions in finance are neither commutative nor additive — saying that addition is not additive sounds very strange, but period addition is not really an addition. All the back and forth on dates to define the compounding period necessarily lead to "not text book consequences".

One of the consequences, that was demonstrated on an example in the above mentioned blog, is the gaps and overlaps in the overnight coverage generated by the fallback. A natural questions from blog's readers and clients is to know how prevalent this effect is among a 'normal derivative book'. It is difficult to decide what a 'normal derivative book' is but we can generate books covering all dates and see what happens. This blog extends the analysis initiated in the previous blog by looking at the effect on a book consisting of 251 swaps with effective date in each business day of 2020. The swaps are USD fixed (semi-annual bond basis) versus USD-LIBOR-1M with a tenor of 2Y. This means one year in which the book builds up, one year in which it is stable and one year in which swaps come to their maturity.

We have three versions of the book: the original LIBOR book, the book after the fallback (in this case considering that the fallback applies as of start of 2020) and a book of OIS with the same effective dates as the fallback swaps start compounding and using similar conventions (same fixed leg as the fallback leg, SOFR compounding with monthly payments on the floating leg). The valuation date is 2019-10-04. The exact valuation date does not really matter, as long as it is before the start of the first swap. The notional of the swaps are USD 10,000.

Like in the previous case, the first step is to look at the daily PV01 of the floating legs.
We start with the simpler case, the OISs. All the composition periods are perfectly aligned and the risk is what you see in any text book: a risk at the start (in one direction) and a risk in the end (in the other direction). The risk is proportional to the time to cash flow. At maximum in our case, the maturity is a little bit beyond 3 years from valuation, so the PV01 is around USD 3 per swap. Due to non-good business days, in some cases two or three swaps mature on the same date and the PV01 in those dates in around USD 6 or 9. This is represented in Figure 1.



Figure 1. Daily PV01 for the portfolio of OISs.

In Figure 2, we present the same graph but with a scale 10 times smaller. This is not a display error, but this is to be able to compare with the other cases later.


Figure 2. Daily PV01 for the portfolio of OISs. Different scale.

We move to the fallback case. According to some descriptions in text related to the transition, the fallback generate risks similar to OISs and should not create any risk management issues. When we apply or daily PV01 to the generated book, we see the risk displayed in Figure 3. The scale of figure 3 is the same as the one in Figure 2. Very large risk, one of them larger than 100 appear. Note that to obtain such a risk, we would require a 100-year tenor swap, 30 swaps with 3-year tenor or a swap with notional USD 300,000 instead of USD 10,000. This the maximum risk, but there are also many days with risks above 50. The risk profile is clearly distinct from the one of an OIS book.



Figure 3. Daily PV01 for the portfolio of swaps after fallback.

For the third book, the LIBOR book, the daily risk is displayed in Figure 4. There are also spikes of daily risks. Even if LIBOR is the main benchmarks for interest rate derivative, this representation of the risk is probably not familiar and certainly does not appear in most text books. The origin of this risk is again the issue with adjustment for non-good business days. The LIBOR periods do not correspond exactly to the swap accrual periods and payment dates.


Figure 4. Daily PV01 for the portfolio of LIBOR swaps.

This risk has been present for as long as LIBOR swaps have been traded. In term of size, the sum of absolute values of all the risk after fallback is about twice the sum of absolute value in the LIBOR case. But, and maybe more importantly, the LIBOR fixes in advance and those daily sensitivities have an impact only in term of the expected rates over those periods. In the case of SOFR, the composition is in-arrears, so the impact is not on the expected value, but on the realized value which is a lot more volatile. Not only the fallback PV01 are larger but they apply to the more volatile realized rates and not to the smoothed by expectation LIBOR rates. The LIBOR has not only an effect of average by accumulation of days over a tenor but also an average effect of expectation.

The graphs reported up to now do not correspond to the standard representation of risk on a trading desk or in a risk management system. The most used representation is as market quote bucketed PV01. We propose those representation below for the fallback and OIS portfolios where we have changed the notional of each swap to be 1,000,000 USD. As can be seen, the difference is very small. In total, there is around USD 1 difference over an almost USD 50,000 risk; the largest difference on any bucket is USD 42. No market maker would hedge the USD 42 risk, but would a market maker look at a USD 10,000 systemic daily risk - which is the maximum risk reported above for the fallback portfolio?


Figure 5. Bucketed PV01 for Fallback and OIS.

It is also important that those daily risk are not appearing randomly because of large trades in the book, they appear systematically because of the vagaries of the calendar. In a calendar with all months of 30 days and weeks of 10 days, those issues would not appear. Maybe the French Republican Calendar should be reinstated to facilitate the LIBOR fallback!

The risk has been displayed as set of daily PV01. Can we also represent the weight of the different days? If the risk is not uniform, it means that some overnight periods are more important than others. What are those periods and what is the size of those under and over-weights? This is represented in Figure 6. For the fallback and OIS portfolios, we have represented the weigh of each overnight period in the 3-year period. The OIS representation is very clean, days weights increase as we add trades in the book, stay constant at 251 (the number of trades) for a year and decrease smoothly after. The representation for the fallback portfolio (in red) is a lot more chaotic. If we look at the middle year, there are many days with a weight of 251, but there are also many days with weigh well below and well above that level. The maximum weight is 292 on 2020-12-23 — this is 41 more than in the OIS case or 16% more — and the minimum weight is 211 on 2021-03-24. Hopefully nothing bad will happen to SOFR on those dates. You can find other interesting dates:  a weight of 282 on 2020-12-24 — i.e. over a 3 day Christmas week-end — or a weight of 227 on 2020-01-29 — i.e. over a 3 day month end.



Figure 6. Portfolio daily overnight count for Fallback and OIS.

Now that this Christmas tree-like has been interpreted, does what it represents transpires to you from the fallback rate adjustment rule book? If not, maybe it would be beneficial for you to discuss all those elements with professionals that have investigated them and many others minutiae for several years.



All the graphs and figures reported in this blog have been obtained using production grade code and market data. The fallback trades are produced using Fallback Transformers tools and libraries developed since 2018. Contact us for more details about those tools.


  1. Fallback transformers - Introduction
  2. Fallback transformers - Present value and delta
  3. Fallback transformers - Portfolio valuation
  4. Fallback transformers - Forward discontinuation
  5. Fallback transformers - Convexity adjustments
  6. Fallback transformers - magnified view on risk
  7. Fallback transformers - Risk transition
  8. Fallback transformers - Historical spread impact on value transfer 
  9. Fallback transformers - A median in a crisis
  10. Fallback transformers - Gaps and overlaps  


Don't fallback, step forward!

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

Tuesday, 26 May 2020

Marc's presentation at the Online Interest Rate Reform Conference

Marc Henrard will present a seminar at the

Online Interest Rate Reform Conference


which will take place from Monday 13 July to Friday 17 July 2020. The agenda of the conference can be found on the organizer web site:




Marc's talk, will be titled Discounting Big-Bang: Quant Perspective and Convexity Adjustments.

Agenda:

  • Collateral and discounting big-bang process
  • Valuation impacts: theoretical clean process
  • Valuation impacts: practical dirty process
  • Transition and convexity adjustments


Note added 2020-08-18: The developments underlying the presentation are detailed in a paper that has been accepted for publication in Risk.Net.

Sunday, 24 May 2020

Benchmarks in transition videos: Episode 8 - LIBOR fallback: value transfer

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 eighth episode is dedicated to the value transfers generated by the new fallback mechanism and the difference between cleared and non-cleared market.




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



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Friday, 15 May 2020

muRisQ quoted in ISDA consultation summary

The Summary of Responses to the ISDA 2020 Consultation on How to Implement Pre- Cessation Fallbacks in Derivatives has been published yesterday 14 May 2020. There were 142 respondent. muRisQ is among the four Professional Services/Trade Association to have answered and the only respondent from Belgium.

Like in previous consultation summaries of responses, muRisQ responses are largely quoted in the document. A first version of the answer appeared on Marc's blog:  Pre-cessation it will be :(

One of the summary sections provide an highlight of the reason behind our negative answer to the pre-cessation question:
51.In contrast, a European professional services firm emphasized that “[i]n the current master agreements, the only event that leads to a fallback is the non-publication of the rate, there is no notion  of  announcement  date  and  even  less  pre-cessation  trigger.  A  pre-cessation  trigger  forces  extra  complexity  and  increases  the  fragmentation  of  the  market.  Legacy  trades  only  have  non-publication  as  a  trigger,  adding  a  pre-cessation  trigger  create  a  discrepancy  between  the  trades  under the new definitions and the legacy trades. The discrepancy would make it more complex to hedge the legacy book. A new fragmentation of the market will be created.” This entity noted, “To achieve the required exposure on new trades, the fallback has to be trigger as late as possible. Any pre-cessation trigger is a negation of the trade existence itself. The LIBOR fixing, even if not perfect or deemed not representative by a third party – e.g.,  a regulator – is better than a fixing based on a RFR plus a spread which is not credit and liquidity dependent. Fallback should be a last resort mechanism  and  used  only  in  last  resort.  The  pre-cessation  event  is  not  an  event  requiring  last  resort. The estimation by a single entity, even a regulator, without review and recourse mechanism in place, regarding a major interest rate standard that has been working for more than 30 years and is still working, should not be consider as a case of last resort.”



Don't fallback, step forward!

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

Thursday, 14 May 2020

muRisQ in the press

An article related to LIBOR/SOFR transition published today in Risk.Net quoted muRisQ. The article is titled "SOFR phase-in for cash products sparks ‘mismatch’ fears". muRisQ provided to the leading magazine on derivatives data related to the transition they could not obtain otherwise. The data is quoted in the text and provided as a graph. We published a similar graph yesterday in Compounding with offset.

Risk.Net turned to us to access data they could not obtain from traditional data provider like Bloomberg. The data has been computed from our production grade libraries. Some examples of the usage of those libraries are provided in the 'analysis' repository provided open source by Marc on Github: https://github.com/marc-henrard/analysis

Wednesday, 13 May 2020

Compounding with offset

The latest proposal related to the IBOR fallback in case of cessation is to include an offset in the overnight composition period. As discussed in previous blogs, this on paper offset may not lead to actual offset on the payment date (see Fallback and same day payment?) and will generate gaps and overlaps between risk periods.

The offset will also be applied to the historical spread used in the fallback. It means that the spread used in the fallback will be impacted by three distinct features: credit/liquidity, market misestimation and offset. The first two have been discussed extensively in different blogs and publication, the third one is new. The interest rates used to measure the spread are related to different periods. Depending if the monetary policy is in a rate increase or a rate decrease cycle over the 5-year lookback period, the intuitive spread will be overestimated or underestimated.

The graph below is the time series of the spreads since SOFR/pre-SOFR has been published (August 2014). As usual in my graphs, the dates reported are the LIBOR fixing dates (not the maturity date) and the SOFR related numbers stop 3 months ago because of the "in-arrears" feature.



The second graph is a focus of the offset impact. Two time series of spreads are computed: one with the two business days offset and one with zero business day offset. The spreads with offsets are a little bit bumpier, potentially due to difference in length in the LIBOR and ON periods.




All the graphs in our blogs are produced by production grade libraries. Our libraries include the Fallback Transformers which allow to apply the exact fallback details to actual trades and portfolios. The transformation details include overnight composition, period offset, spread applicable, and discontinuation date. It is suitable for what-if analysis and risk management.



Don't fallback, step forward!

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

Friday, 1 May 2020

Benchmarks in transition videos: Episode 7 - LIBOR fallback: spread

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 seventh episode is dedicated to the spread part of the fallback.




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



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Tuesday, 28 April 2020

Bespoke course: 3000

We have just received an email from a large training provider. They indicate
Bespoke training for you and your team starting at GBP/USD/EUR 10,000*! *pricing dependent on topic and group size.
On our side, we can say
Bespoke training for you and your team starting at GBP 3,000/day*! *pricing not dependent on topic and group size.

The course are always provided by our in-house experts and, from our training page:

Agenda tailored to your needs. Detailed lecture notes.
Associated to open source code for practical implementation.
Training in English or French

We are an (fiercely) independent management owned advisory firm and the trainings reflect that independence. We don't have hidden agenda and are free of conflict of interest.

In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

We have provided public and in-house workshops/courses/seminars in Africa, America, Asia, Europe, and Oceania (special discount for any client base in Antarctica!).

Some of our courses are described in our training pages. Over the past year, the most popular ones have been

In all cases, the course are updated with the latest market information and are fully flexible.

You can check some of our introduction videos on our Youtube channel.

Note added 2020-11-30: With inflation, increased demand and increased administrative requirements, we have slightly increased our prices recently.

Friday, 24 April 2020

Fallback transformers: gaps and overlaps

The proposed IBOR Fallback Rate Adjustments Rule Book has been published by Bloomberg.

The exact details of the fallback from IBOR to compounded setting in arrears seems slightly different from the version in the latest ISDA consultation. In particular the compounding period is back from the "calculation period" to the IBOR tenor period. The period is defined with an "offset by 2 business days".

In this post, we look at the precise description of the "offset by 2 business days" as its implementation may be different from an intuition of such an offset.

The composition period is defined, first by moving froward from the fixing date by two business days to the spot date. The move forward is in the calendar of the replacing overnight index. For USD, this is already a little bit tricky as for LIBOR the fixing is in GBLO calendar, the effective date is in GBLO and USNY calendar but SOFR is fixed in the USGS calendar. We skip this question of calendar here. From the spot date, the start accrual date for the composition is computed by moving backward by 2 business day, this is the "backward offset by 2 business days" from the consultation. The end accrual date for the composition is computed from this start accrual date by adding the tenor of the IBOR index. For tenors in months, the end date is adjusted modified following.

The feature of this approach is that the backward offset is done on the start date and the end date is recomputed from the start date. Due to non-good business days, week-end in particular, there is no guarantee that the end date for the composition will actually be before the end date of the coupon period. In many cases there will be a same day payment. One example is described in the post Fallback and same day payment?.

In this post we want to focus on the impact of the way the offset is computed on the overnight risk. Because each compounded period for consecutive coupon of a swap is computed with its own offset, there is no guarantee that those periods will fit nicely next to each other. In another blog commenting on the fallback rule book, we mention one such example.

Having added the new fallback rule in our Fallback Transformer library, we can now look at the impact that those periods not fitting exactly has on the risk. Here the risk is a lot more complex that for LIBOR as each day counts, and with SOFR showing spikes at month-end, quarter-end or 15th of the month, the exact day is important.

We use the same example as the one described in the above mentioned blog: Example 1M-IBOR swap over 5-month period: 2020-03-26 to 2020-08-26. The standard accrual periods for the coupons payments are on dates 2020-03-26, 2020-04-27, 2020-05-26, 2020-07-26, 2020-07-27, and 2020-08-26. The accrual periods for RFR compositions (with 2 days offset) are [2020-03-24, 2020-04-24], [2020-04-23, 2020-05-25], [2020-05-22, 2020-06-22], [2020-06-24, 2020-07-24], [2020-07-23, 2020-08-24].

We look at the risk of the swap resulting from the fallback and the risk of a standard OIS starting on 2020-03-24 and ending on 2020-08-24. With those dates, the OIS has exactly the same start and end date as the OIS composition resulting from the fallback. This is true at least at the total swap level. What is happening at the coupon level?

The coupon level is described in the next two graphs. The first one is the OIS risk. In the graph, we represent only the risk associated to the forward rates (not the discounting, which is very small). We look at the risk at the (zero-coupon) rate daily sensitivity, not through a standard Bucketed PV01. The daily feature is important to understand the difference between the two instruments. The risk is viewed from 2018-08-30, this date is not important, it turns out this is the date used in previous blogs.

The swap has a notional of 1 million. Its effective date is roughly 19 months after the valuation date and the maturity date roughly 24 months after the valuation date.The risk profile is exactly what you expect. A large risk at the start, with a value of roughly 1,500 USD/bps and a large risk at the end, with a value of roughly 2,000 USD/bps in the opposite direction. Each coupon payment has a very small risk which would be cancelled by discounting risk.


The profile of the swap resulting from the fallback is a lot more interesting. Due to all the adjustments related to week-ends, the end of one coupon compounding period does not match the start of the next coupon compounding period. In this particular case, each coupon creates large positive and negative exposures at slightly different dates. In some case, there are overlaps between the periods and in other cases, there are gaps between them. Counting positive days for overlaps and negative days for gaps, we have at the 4 intermediary dates, 1, 3, -2, and 1.



Market makers will need to adapt their tools to deal with those gaps. Also, those gaps will not be completely random. Some week-ends will be more favorable for gaps and some more favorable for overlap. You cannot expect a large book to smooth those features out, to the opposite, a large book with not perfectly offsetting trades will tend to accentuate those features.

Note added 2020-05-31: A similar analysis on a large portfolio is available at Fallback transformers - Gaps and overlaps - portfolio version.


  1. Fallback transformers - Introduction
  2. Fallback transformers - Present value and delta
  3. Fallback transformers - Portfolio valuation
  4. Fallback transformers - Forward discontinuation
  5. Fallback transformers - Convexity adjustments
  6. Fallback transformers - magnified view on risk
  7. Fallback transformers - Risk transition
  8. Fallback transformers - Historical spread impact on value transfer
  9. Fallback transformers - A median in a crisis
  10. Fallback transformers - Gaps and overlaps
  11. Fallback transformers - Gaps and overlaps - portfolio version


Don't fallback, step forward!

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

Sunday, 19 April 2020

Benchmarks in transition videos: Episode 6 - LIBOR fallback: adjusted RFR

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 sixth episode is dedicated to the floating rate part of the fallback.




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



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Updates on LIBOR/ON spread

Some updates on the LIBOR/Overnight compounded in arrears spreads. Posted without comments.

We refer to the previous post on Signing the LIBOR fallback protocol: a cautionary tale for the first graph, Forward looking the spread between forward looking and backward looking rates  for the second one and to LIBOR Fallback: a median in a crisis for the third one.





Using the forward ON curves for the next 3 months, the spread is 29.21 bps (computed with the median). The spread if computed with mean would be 35.34 bps, a difference of more than 6 bps.

Wednesday, 15 April 2020

Benchmarks in transition videos: Episode 5 - LIBOR fallback: 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 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 fifth episode is an overview to LIBOR fallback. Three more episodes will be dedicated to the fallback.




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



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Monday, 13 April 2020

Easter

This year, Easter benefits will be reduced to a small set of strange looking eggs.




When times are better, don't hesitate to contact us if you are interested by one of those golf eggs!

LIBOR discontinuation: 2 years to go and calibration

The most talked about date in the LIBOR world, or disappearance thereof, is January 2022. That is 2 years to go!

You may think that there is a problem with my calendar or that I'm still in the mist of new year celebration and I have missed the fact that there is 3 months less than 2 years to go.

But I maintain it is 2 years to go, actually a couple of weeks less than 2 years. In finance there are many conventions to compute the meaning of a tenor. Why is January 2022 separated by 2 year from April 2020 in the LIBOR world? Take a 2 year swap in the most traded currency (USD) with the most traded LIBOR (USD-LIBOR-3M). If you traded a swap on 2-Apr-2020, the effective date was 6-Apr-2020, the last LIBOR coupon will start on 6-Jan-2022 with fixing 4-Jan-2022. The 2-year swaps traded a couple of days ago, on the 2-Apr-2020 were the first 2-year swaps impacted by the January 2022 discontinuation. This justifies the "2 years to go" part of the title.

What about calibration? In a recent post, we indicated that "LIBOR Fallback is not a curve change, it is a contract change!". Does it means that I have to change the contracts/instruments used in my curve calibration? The short answer is "Yes, you do!" If the contracts are changed, with some payments in the swap changed from a "LIBOR fixed in advance" to a "SOFR compounded in arrears with 2-day shift", those details have to be included in the curve calibration. As mentioned above, we have just past the 2-year (swap) mark for the discontinuation date. This is important as it means that on a 2-year swap, now 1/8 of it embed discontinuation. Moreover, if you use 18-month and 2-year swaps in your curve calibration, 1/2 of the 6-month period between those two nodes is impacted. Is the impact large? The only way to know if is to try with actual market figures.

For this we compare three cases: 1) Ignore the existence of discontinuation 2) Take into account the existence of discontinuation for calibration and pricing 3) Take discontinuation into account for pricing but not for calibration in a hybrid way. This last method is incoherent, but may be a natural first step where the change is introduced were it is the simplest.

First we look at the no-discontinuation/no-fallback case. We just use our standard curve calibration procedure. Here to make the things simple and look at one issue at a time we use curves described by zero-coupon rates with linear interpolation on the rate. Obviously for actual market making, you would be more careful on how you calibrate curve, probably using some piecewise constant forward rate and a coherent LIBOR/OIS spread as described in a previous post on "Curve calibration and LIBOR/OIS spread". Here we want to present the difference between the three methods above and the starting point is not our focus as long as we use the same method for all cases.

How does the curve look? The calibration is done as of Thursday 9-Apr and we display the USD-LIBOR-3M forward rates (not the zero-coupon rates) and the SOFR 3-month period forward rate on the same period as LIBOR. The x-axis is the LIBOR fixing date; there is one rate for each good business day. We observe a standard pattern with kinks. The LIBOR/OIS implied spread is represented with the small dots.



We now move to the discontinuation. For that, we need to introduce a couple of hypothesis: the discontinuation date and the adjustment spread. We have selected 1-Jan-2022 for the discontinuation and 25 bps for the spread. The difference is immediately obvious. First there is a clear jump on the graph, from a market implied spread based on the economical reality of LIBOR to a legal contract implied constant spread. After the discontinuation, the spread is constant. The jump in this calibration is more than 15 basis points. This is called in some places a "cliff-effect", it is a cliff-effect only in the graph, not economically. A given instrument has a given fixing date, e.g. the dreaded 4-Jan-2022 mentioned above, you know already that date, you know that it will be after the discontinuation (under our hypothesis of discontinuation on 1-Jan-2022), so there is no surprise, there is no cliff, this will be a SOFR + spread payment. You would be surprise if, like in the first graph, someone was telling you that the value is depend on the LIOBOR economical reality on that date! The cliff can only come from ignoring reality in your calibration/valuation.



Is there a big difference between the different cases? For that we focus only on the period from 1-Jun-2021 to 1-Jun-2022. The rates are displayed in the figure below.

Before that period, all the methods give the same results. The swaps up to 18-month tenors are not affected by the fallback. If we look at longer term, there will be an impact, but a lesser one. It is really around the discontinuation date that the difference is clear. In the graph we have added also the hybrid result with fallback on the pricing but not on the calibration. We see that around the discontinuation date, before it, the no-discontinuation approach is overestimating the rate and after it, it is underestimating it. The difference between the different cases is up to 10 basis points. The market rates are matched perfectly, so you don't see the difference on standard tenor swaps. But if you have to price a non-standard instrument, e.g. a FRA with a start date just before or just after the expected discontinuation date, you may mis-price it by as much as 10 basis points.

Conclusion: Calibrate wisely and make sure that the instruments you price and those you are calibrating to are taking the LIBOR fallback/discontinuation into account for the contract description.

Saturday, 11 April 2020

Benchmarks in transition videos: Episode 4.b - CCP big bang - USD

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 fourth episode (part b) describes the PAI and discounting big bang at CCPs for USD.




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



In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Wednesday, 8 April 2020

Benchmarks in transition videos: Episode 4.a - CCP big bang - EUR

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 fourth episode (part a) describes the PAI and discounting big bang at CCPs for EUR.




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

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 third 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

Mandatory IM: Category 5 and 6 delayed by one year

The BCBS has proposed a deferral of final implementation phase of the mandatory IM requirement for non-centrally cleared derivatives. The BCBS press release can be found at: https://www.bis.org/press/p200403a.htm

The BCBS deferral is in line with the proposition that Marc made at the QuantSummit and quoted in the press.

As mentioned previously, we have developed our own code related to a Standard Initial Margin Model (SIMM) used by most of the banks under mandatory IM (currently category 1 to 4). Our implementation is AD compatible and provides the derivatives/sensitivities with respect to all the inputs (all the input amounts).

Note added: By doing some reviews, we have also noticed that some open source code for its computation contains bugs related to the computation of correlations (string comparison bugs).

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, it 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.