Newsletter of the Bachelier Finance Society

Volume 13, Number 1, January 2021

ONLINE GENERAL ASSEMBLY

There will be a virtual General Assembly on Thursday, 14 January 2021, 18:00 (GMT +1) where the Executive Committee can inform the membership about what has happened within the Bachelier Finance Society during the past months.

JOB POSTINGS

The aim of these postings is to create a forum for the dissemination of information on academic and industrial positions related to mathematical finance, across different disciplines and different geographical regions. Please submit any job advertisements you are aware of to jobads@bachelierfinance.org, preferably in plain text and sending the link to the website containing all the information. Updates and new items appear continuously at: bachelierfinance.org/forum/jobs

Faculty position
Worcester Polytechnic Institute
Deadline: January 15, 2021

Research Assistant in Quantitative Finance
University of Freiburg
Deadline: February 5, 2021

Call for Submissions – Nicola Bruti Liberati Prize
https://www.bachelierfinance.org/nicola-bruti-liberati-prize
Theses defended in 2019 and 2020 must be submitted no later than February 1, 2021.

The Society maintains a list of books, book reviews and journals at: https://www.bachelierfinance.org/publications. Members who would like to have their books added to the website, should please let us know.

Recently published books

Cheng Few Lee, John Lee (Eds.)
Handbook of Financial Econometrics, Mathematics, Statistics, and Machine Learning
World Scientific (2020), ISBN 978-981-12-0238-4

Leading article:

Failures in Benchmark Transitions

Marc Henrard

For interest rate quants, we are living in exciting times: all interest rate products are now exotics, understanding the idiosyncrasies of each payoff is like a detective assignment; in this time of uncertainties, our future job relevance seems guaranteed.

Every single interest rate product, even the most vanilla ones, require an in-depth quantitative analysis. The payoff of all the products are uncertain, and not only uncertain in the stochastic sense or in the credit risk sense, issues that we are familiar with, but uncertain in the more fundamental sense that we don’t know the rules and they are decided by someone else. Not only are we short options, but we don’t know options on what and we don’t know who is long. An interest rate derivative contract is not anymore a two parties agreement, but there is often a third party involved and in some cases even a fourth and a fifth party join.

Take a simple London InterBank Offered Rate (LIBOR)-linked interest rate swap. You traded with a counterparty on a bilateral basis under master agreement and loaded the trade on a Central Clearing Counterparty (CCP) a couple of years ago. Then the Alternative Reference Rate Committee (ARRC) decided that the USD reference rate should be the Secured Overnight Financing Rate (SOFR) and not the Effective Fed Funds Rate (EFFR), your collateral rate is changed by the CCPs, the International Swaps and Derivatives Association (ISDA) is doing a consultation on LIBOR fallback, the results are pushed on your trades through the CCP or a quasi-mandatory protocol, the Financial Conduct Authority (FCA) wants powers to impose a “non-representativeness” criterion that you have to accept, then the CCP changes its mind and decides that it will not actually use the ISDA-designed fallback but its own version because it cannot manage the risk of the first fallback. Unfortunately, the couple of lines above are not finance fiction, they describe the reality of the last four years! Your innocuous trade with a counterparty of your chosing is now a trade with six (6) parties involved — yes, when I mentioned a fifth party above, I was one short — and many almost un-hedgeable features. In this column, I would like to go through some of those issues.

This is all the excitement I was referring to in the opening sentence. We, interest rate quants, have to model all those issues. Certainly a job security for many years! By the way, for other asset class quants, variation margins are mandatory since 2017; variation margin means overnight benchmarks appear in the valuation of all derivatives and the joy of benchmark transition has contaminated or will/should contaminate all the other asset classes.

This job security was unfortunately engendered from failures. As much as vaccine developers have a job security for the coming years, I’m sure that most of them would have felt better without it. To some — less dramatic — extent, this is how I feel today. The path I propose to take here to go through the benchmark transition overview is a path of some of those multiple failures.

Failure 1: Not writing clean contracts

Life means changes. The theory of evolution is based on that. Any long term planning based on an unchanged world is doomed to fail. Financial contracts related to benchmarks, overnight or IBOR, have been written up to recently as if the world was immovable and today’s benchmarks and behaviours would exist forever. Looking for example at today’s definition of LIBOR payments, the fallback language is something like “If LIBOR is not published, the Calculation Agent will request the principal London office of each of the Reference Banks to provide a quotation of its rate”. Meaning that for ever such a “LIBOR rate” will be a natural question and all banks will be happy to provide such a service for free. That is a very weak mechanism. You can tell me that the current situation is extraordinary and could never have been forecasted, and I could answer that I never asked for a forecast, only a stress resilient mechanism; but I will not do so. My point is that the Wheatley report dates back from 2012 and the Financial Stability Board Reforming Interest Rate Benchmarks dates back from 2014. At the beginning of 2021, we still don’t have a meaningful fallback language. At this stage we expect to have a fallback language that is apparently meaningful from a legal perspective — but a horror from a risk management perspective — taking effect on 24 January 2021. This is a very long period to start having partially decent contract languages.

Would you, dear fellow quant, start you main quantitative finance opus with ambiguous definitions? I guess the answer is no. But if you want to price in practice LIBOR derivatives you need to start with a formula like the one I used in Henrard (2019):

\( N^c_s \mathbb E^{\mathbb X}\big[ (N^c_w)^{-1} f\left(\mathbb 1\{d > \theta\} I^j(\theta) + \mathbb 1\{d \leq \theta\}{\color{red}?}\right)\big| \mathcal F_s\big].\)

The important part of the above formula is the question mark around the end. That question mark is not a typo, it is the most precise formulation I can provide. It is the state of our market!

Nowadays, standard quant job requirements include legal document reading skills to understand the quantitative impacts of regulations, contract details, and master agreements including their supplements. But reading skill is meaningful only if writing exists. And that leads me to the second failure.

Failure 2: Not asking quants about contract writing

The “regulations, contract details, and master agreements” that I mentioned above need to be written. To achieve the goal of a wonderful world with a perfect fallback mechanism, the writing has not only to have correct spelling but also to avoid unintended hell.

Looking at the history of the LIBOR fallback ISDA’s consultations, we can only wonder who looked for the potential hell. The first consultation indicated

the relevant RFR observed over the relevant IBOR tenor
(ISDA consultation, September 2018.)

The terms “observed over relevant IBOR tenor” were not defined. The next consultation indicates:

the fallbacks will be determined by reference to the Calculation Period (as adjusted for “backward-shift” or “lockout”) as opposed to the IBOR period
(ISDA consultation, September 2019.)

The term “Calculation Period” was not defined. The terminology “IBOR period” is not coherent with the “IBOR tenor” used previously but it seems that the new consultation refers to the same item as the first consultation.

A later EUR consultation refers to

the compounded setting in arrears rate approach with a backward-shift adjustment
(ISDA consultation, December 2019.)

Any mention of tenor or period has disappeared.

The final version of the supplement indicates

Fallback Rate […] as most recently provided or published as at 11:30 a.m., London time on the related Fallback Observation Day

No mention of “period”, “tenor” or anything similar anymore, simply the indication that someone, somewhere, for some fee will provide the required magical number. That magical number methodology is provided in the Bloomberg “IBOR fallback rate adjustments rule book”. Did I tell you that there were 6 parties involved in your vanilla trade? Sorry for my earlier mistake, there are actually 7 parties involved, and you have to pay at least 20,000 USD/year to this late uninvited newcomer. He has obtained an exclusive license for it and is allowed to ask you as much as he wants for a couple of multiplications and additions related to public information. And that document indicates “[…] no assurance can be given that […] circumstances will not arise that would […] necessitate a modification or change of such methodology or termination of the Rate Adjustment.” But I don’t want to anticipate myself, changes are Failure 4, and we are only at Failure 2.

What is the actual text in this new document?

Accrual Spot Date means, with respect to an IBOR, its Reference Rate, Tenor and a Rate Record Day, the Reference Rate Business Day that is the Reference Spot Lag number of Reference Rate Business Days immediately following such Rate Record Day. For the avoidance of doubt, if the Reference Spot Lag is 0 (zero) and such Rate Record Day is not also a Reference Rate Business Day, then the Accrual Spot Date is the Reference Rate Business Day immediately following such Rate Record Day;
Accrual Start Date means, with respect to an IBOR, its Reference Rate, Tenor and a Rate Record Day, the Reference Rate Business Day that is the Offset Lag number of Reference Rate Business Days immediately prior to the Accrual Spot Date;

and you have several pages of this. If you spend a couple of days reading it — I have done it and it explains some of my night crying — you notice that the impacts of all those embedded definitions are that all your nicely designed products are becoming a mess of Frankenstein-like modified periods.

Coming back to the supplement, there is in the definitions a

Fallback Rate […] as most recently provided or published.

Those “most recently” words are extremely important and newcomers in the definition. Because the main mechanism was ill-conceived, you may have to pay a certain amount before you know what that amount is. In quant speak, the amount to be paid is \(\mathcal F_t\)-measurable and not \(\mathcal F_u\)-measurable but paid in \(u<t\)! With the addition of those two words, if something is not measurable, you just take the last available thing which is measurable to replace it. Simple, isn’t it? Take for example a Forward Rate Agreement (FRA) which pays a forward looking LIBOR dependent amount just after its fixing. With the introduction of the “most recently”, you have to go back in time roughly the LIBOR tenor period to start the composition and use a rate on a period different from the LIBOR one, with no overlap at all. The economical reality behind the instrument is completely altered. Similar issues appear for LIBOR in-arrears and range accruals. Also this most recently is throwing out of the window any schedule in your long term swaps. Instead of a nice 10-year swap over a continuous 10-year period, you have a combination of 40 3-month swaps on periods with gaps and overlaps. If this is not obvious from the above legalese, I invite you to have a look at the graphs in my blog “Fallback transformers: gaps and overlaps”. If you are risk managing a book of vanilla derivatives, after that you may think that horror movies screenwriters lack imagination.

Failure 3: Not listening to quant screaming

OK, I have already started this section. I have been screaming for a couple of paragraphs. If you listen carefully, you may even hear quants crying at night; at least I have done so for many months now. The issues that I describe here are not things that require long mathematical finance developments and can be understood only by some initiated. Those are issues easily understood by anyone having a calendar (with the week-ends clearly indicated) and that has spent some time trading or risk managing swaps. Not paper managing, actually managing the valuation formulas, implementing all the conventions in a system and managing liquidity on a day to day basis. Those are not hidden issues discussed behind closed doors, the exact problems that seem to be “discovered” at each step have been described for many years. I can refer to my Quant Perspective (Henrard 2018) for some of those early screams. The worst of it is maybe the attempt to force those ill-designed mechanism on unsuspecting end-users through a protocol.

The failure was not only in not listening, it is also to some extend forbidding others to speak or listen. None of the consultations contained a balanced analysis of the issues at play; reading them carefully it is possible to infer the answer that the consultation promoters would like to hear. At times, it sounds like promoters would like to restrict the responders. I have answered to public consultations and for one of them received from a regulator/central bank an answer indicating that they would first like to clarify in which capacity [I was] replying to the public consultation and that the public consultation is addressed to “interested parties’‘. To answer a public consultation, you need to have a conflict of interest! You don’t need to be knowledgeable, bring a wealth of experience or provide a service to the public for free, you need to be “interested”!

There is currently an ECB organised consultation about “ESTR-based EURIBOR fallback rates”. The consultation is related to non-derivative — e.g. bonds and loans — fallbacks. In the consultation document, a number of alternatives are presented. Among those alternatives are standard overnight FRN conventions and a different one called “Principal adjustment”. The latter is a methodology that I like and have proposed (or probably re-proposed) a year or so ago in a blog. The idea of the convention is to include the interests into the principal (or notional) on a periodic basis and simultaneously pay part of the principal; that payment can be viewed as an advance on the final interests. It could be described as a zero-coupon — more exactly a one-coupon — instrument with notional amortisation. The ECB document presents the methodology as having Significant operational complexity, More complex and less transparent calculation and Relevant hedging issues expected. The “small” problem is that all those characterisations are simply wrong. The method has the same complexity and transparency than the main methods proposed and is as easy to hedge. One of the main issues about in-arrears overnight composition is the fact that the interest amount is known only at the end of the period, a couple of days before payment. That issue is solved by the Principal adjustment convention for all but the last period. The periodic payment can be decided at the beginning of each period or even earlier. ​Why does the central bank not engage in stronger and more careful independent expert review before publishing its consultations wording? What is the value of answers to consultation questions the premises of which are counterfactual? It would be beneficial to have some kind of public consultations peer review. Consultations are read by many academics and practitioners, why not take advantage of this? Most of the consultations official answers are not public but even if they were, they would come too late. It would be helpful to provide an open space where feedback or technical analysis on the questions can be presented by independent — or not so independent — parties before they are proposed to consultation.

Of course, the list of screams does not finish here. We could add the many issues, including on non-linear products, for example the ones described in Piterbarg (2020).

Why should the world listen to quants? Let the master of us all answer the question:

Si […] j’ai comparé les résultats de l’observation à ceux de la théorie, ce n’était pas pour vérifier des formules établies par les méthodes mathématiques, mais pour montrer seulement que le marché, à son insu, obéit à une loi qui le domine ; la loi de la probabilité.
Louis Bachelier, (last sentence of) Théorie de la spéculation, 1900

Personal translation:
If […] I compared the results of the observation to those of the
theory, it was not to verify formulas established by mathematical methods,
but only to show that the market, unwittingly, obeys a law that dominates it:
the law of probability.

I don’t claim that quants know better than everybody else, only that they have a tool to hear the market; that tool is called “quantitative finance”.

Failure 4: Change plans

After several years of not asking and not listening, the obvious becomes obvious and plans need to be changed. I have already mentioned the many changes in the ISDA fallback descriptions. Let me shift a little bit my subject and move to CCPs. Since the financial crisis, CCPs have been imposed on the market from a political side:

All standardized OTC derivative contracts should be traded on exchanges or electronic trading platforms, where appropriate, and cleared through central counterparty by end-2012 at the latest.
(G20 declaration, Pittsburgh, September 2009)

The CCPs are becoming de facto the risk managers of the world, they are now a mandatory path to trading vanilla interest rate derivatives. CCPs have in the past vaguely said that they would implement the ISDA fallback once it is definitively agreed. And now we learn that

LCH is planning to automatically convert all LIBOR-referencing swaps to directly reference compounded-in-arrears versions of their respective risk-free rates when the benchmark ends, instead of relying on contractual fallbacks to deal with legacy contracts.

CCPs have, rightly, determined — maybe after reading my blogs — that the proposed fallbacks are unmanageable from a risk and valuation perspective. Saying; for example

[…] the old-style contracts […] may undermine confidence in our default management capabilities
(David Horner, head of risk at LCH SwapClear.)

Now we are in the situation where the long discussed ISDA plan, that took 3 years to agree, is so ill-designed that the world’s risk managers think that its existence is such a threat that they need to be dispensed with, even before it comes into existence. CCP cleared swaps represent more than 90% of the notional of vanilla swaps. The fallback discussion had a real meaning only if it was applied to the vast majority of swaps, which is not the case anymore. If the mere existence of old-style contracts undermine “confidence”, how can we have confidence in the very same CCP capacity to “compensate the losers with cash payments” for old-style contracts in a fair way? Someone is afraid of the fallback risk and valuation in a second order situation (conditional to default) and to get rid of that risk, he will value its impacts and push his decision on the market participants as a first order problem (daily risk management)! We are back to square 1! Or more exactly, we are back to failure 2! Which quant has accessed those plan changes and the embedded value transfers? Which quant has designed the valuation framework? Was it carefully model validated? Can I see the in-depth analysis of all its direct and indirect consequences on valuation and risk management, not only for the CCPs but for the derivative market and users in general? Who will manage the basis between all the different fallback mechanisms? How long will those new swaps be under guarantee? What is the return policy?

For significant changes, we can also go back to the 2017 ARRC’s paced transition plan that included “Step 4: CCPs offer choice between EFFR PAI/discounting or SOFR. (Planned Q1 2020). Instead of that paced transition, a big-bang transition where CCPs unilaterally imposed a one day transition and its value was implemented. Such a big-bang created significant operation and risk management issues for users. On top of this (almost) manageable issue, it also created value transfer for bilateral swaptions that rely to CCP mechanisms for settlement. That value transfer had its origin in Failure 1 (not writing clean contracts) but was aggravated by the unilateral change of plan (Failure 4). Will the above mentioned changes on fallback create another value transfer?

How many times will we loop around failures 2, 3 and 4 before deciding that “enough is enough”?

Failure 5: Never acknowledge failures 1 to 4

The next step should appear obvious from the previous ones. It is of the utmost importance to never acknowledge Failures 1 to 4! Don’t say that regulators or lawyers could write a rule that has unintended consequences in a domain that they are ignorant about. Never doubt the omniscience of the higher powers.

If you search the web today for “ARRC’s paced transition plan”, you don’t find the original 6 steps plan with Step 4 described above. You find a 5 steps plan than says that CCPs “converts discounting and PAI/PAA from EFFR to SOFR on all outstanding cleared USD-denominated swap products”. The original plan failures have been removed, in a very 1984-like “Who controls the past controls the future. Who controls the present controls the past” way.

The issue of value transfer in swaptions due to CCP changes on swaps is considered “not their problem” by CCPs. ISDA has never published a detailed document with the risk and valuation issues brought by the fallback and its related protocol. How can we learn from the past if the past is hidden?

From a bleak past, we can try to move to a bright future. What new year wishes can we make? I don’t think that screaming loader is helpful. Personally my wishes are in the direction of transparency and freedom. On the transparency side, at the very least we should require all preparation technical documents for consultations and regulations and answers to consultations to be made public (subject to an opt-in/opt-out mechanism decided by the authors). On the freedom side, all new proposals should include a flexible mechanism such that if something is not working as planned, each participant can decide how he wants to adjust, without a centrally imposed, probably ill-suited, process.

If this column was written in French, as Louis Bachelier would have done, I would say “On a échoué !“. A standard translation in English would be something like “We failed“, but this is not a perfect translation. The French “on” is a subtle mixture of a singular personal pronoun which represents a plurality of people with a hint of “we” in it, vague enough that it is not clear if the author includes himself in the plurality. This is exactly the meaning I would like to convey here:

On a échoué!

This failure is not due to lack of skills, goodwill or hard work. There is plenty of all of them. But probably they have not been called at the right time and in the right order in this long process.

On this positive note, all what is left to me is to wish you all a

Happy new year!

Acknowledgments: The author thanks early readers for useful comments. All remaining errors, misunderstandings, opinions, point of views and unintelligibilities are his.
_____

Marc Henrard is the Managing Partner at muRisQ and a Visiting Professor at University College London.

No quotation of this document is allowed without properly identifying the source and the author.

We would like to draw your attention to this event related to the LIBOR transition:

The mathematical finance group at Université de Paris/LPSM has the pleasure to open the year by a special online event, where four top experts from industry and academia: Claudio Albanese, Ernst Eberlein, David Gorans, and Marc Henrard, will share their views on the Libor transition.

Details and registration (free but mandatory) can be found on the website:
https://www.louisbachelier.org/evenement/the-universite-de-paris-libor-transition-online-workshop/

UPCOMING CONFERENCES

This list contains conferences related to mathematical finance that take place in the next three months. A full list is available at https://www.bachelierfinance.org/conferences. Please let us know of conferences we are not aware of and include a URL for the event.

10th Western Conference on Mathematical Finance
January 15–18, 2021
online

22nd Workshop on Quantitative Finance QFW2021
January 28–29, 2021
online

Energy Finance Italia Edizione 6 (EFI6)
February 22–23, 2021
online or hybrid in Brescia, Italy

Commodity and Energy Markets Association (CEMA)
June 17–18, 2021
online

10th General AMaMeF Conference
June 22–25, 2021
Padova, Italy

6th Symposium on Quantitative Finance and Risk Analysis (QFRA 2021)
June 23–25, 2021
Crete Island, Greece