Game of Benchmarks: LIBOR and IRON thrones

I will present a seminar titled Game of Benchmarks: LIBOR and IRON thrones at the UCL Financial Mathematics Practitioners Seminar. The seminar will take place on Wednesday 22 November 2017 from 4.10pm to 5.00pm at 25 Gordon Street (London) -- room D103.

Updated 2017-12-05: The slides are available from the page of the seminar referenced above. The direct link to the slides is https://www.ucl.ac.uk/maths/graduate-students/msc-financial/m_henrard_game_of_benchmarks_LIBOR_and_IRON_thrones


Alechinsky and Margin

Today I visited an exposition on Pierre Alechinsky, a Belgian artist. Some of his works are visible at the MoMA.

Among the frames, there was the poster of a previous artist exposition in New York titled  
Margin and Center.

Margins are following me everywhere now, even in art shows!


Algorithmic Differentiation training

I will present a training session on AD in December.
Location: Warsaw, Poland
Date: 13 December 2017 (full day)
Organizer: CEETA - Tomasz Dendura

Algorithmic Differentiation in Finance

Algorithmic Differentiation (AD) has been used in engineering and computer science for a long time. The term Algorithmic Differentiation can be explained as the art of calculating the differentiation of functions with a computer. AD is now also a standard tool in quantitative finance.

The workshop presents AD from a practical point of view and targets quantitative analyst, risk manager and developers working in finance. The focus is on the foundation of the method and the idiosyncrasies of the applications in finance. Different implementation alternatives are presented, allowing each participant to adapt the general method to his needs.

  • Introduction
    • AD is magic (or not)!
    • Exact derivatives
    • Finite difference
    • Development time v running time
  • The Principles of Algorithmic Differentiation
    • Derivative
    • Composition
    • Algorithm: assignment
    • Algorithm: branches
    • Algorithm: loops
  • Application to Finance
    • Basics: Black formula and SABR
    • Interest rate sensitivities
    • Monte Carlo
  • Automatic Algorithmic Differentiation
    • Standard Algorithmic Differentiation by Operator Overloading
    • Adjoint Algorithmic Differentiation by Operator Overloading
    • Automatic Algorithmic Differentiation applied to finance
    • Mixed Algorithmic Differentiation implementations
  • Application to Finance (2)
    • Automatic Algorithmic Differentiation applied to finance
    • Non-derivatives with respect to inputs - sticky smile
  • Calibration
    • Curve calibration
    • Model calibration and implicit function theorem: exact calibration
    • Model calibration: least-square

The lecture notes of the workshop are provided in the form of the recently published book Algorithmic Differentiation in Finance Explained, Palgrave (2017).

The workshop is backed by open source code (freely available on Github). On one side, the code is composed of tutorials of increased complexity. Those tutorials present the different fundamental principles of AD and propose several implementation for each of them. Another side of the code used is a full production grade quantitative finance library using AD as one of its tools. That library is used in production by hedge funds, banks and clearing houses.

Learning outcomes:

The mathematical foundations of Algorithmic Differentiation methods.
The effective application and use of AD in finance.
Beyond vanilla implementation: further efficiency gains specific to finance.

I'm also propose the course as in-house training. Don't hesitate to contact me for more details.

Game of Benchmarks: Season 1 - Episode 4: Transition and transition team.

Transition to a different world is difficult, more difficult than inventing a better world from scratch. In this episode, I’m looking at the transition.

There are probably more questions than answers. But, as you know,

In mathematics, the art of posing a question is more important than the art of solving one.
Georg Cantor, 1867.

Is transition important?

Valuation of flow derivatives, and in particular Libor linked derivatives, and the associated collateral discounting framework are vanilla in name but certainly not simple if you have to implement them from first principles. The impact of features that were considered before the Great Financial Crisis (GFC) as “details” are nowadays very significant. You can not simply replace one benchmark by another and hope for the best. There are numerous items to take care of, like valuation framework, non linear effects, convexity adjustment, risk management strategies, liquidity, regulatory impacts, etc. I don’t know if, from a purely legal perspective, you can replace a benchmark with something else by using a legal trick - like an act of parliament, as suggested by some lawyer — but certainly not from a financial perspective.

From a financial perspective, changing a benchmark will create winners and losers. Selecting a new benchmark and imposing it on everybody (with or without spread) may look easier from an external eye, but is only removing some symptom on the short term, not the disease. Derivatives are not only a legal document or a value, there are mainly a risk management strategy, often spanning over several decades. To successfully deal with a change of benchmark, one needs to create new strategies for those decades of risk management.

Behind each derivative linked to a benchmark there is a risk management strategy (or risk taking one, but this is a very small part). If Libor is changed or discontinued, one has to review each contract individually, reassess the risk management strategy - including all the collateral, regulatory and valuation aspects - and have a bespoke new strategy. Imposing an external artificial solution is not helping on that review. If your review concludes that the proposed solution does not fit perfectly your needs, you have anyway to engage in discussion with the trade counterparts on what to do; if the proposed solution fit exactly the strategy you designed, there was no need of an external solution as you had created it already. Whatever the proposed default solution is, I don’t see how it could fit the requirement of the majority. Not that I know that the choice that still has to be made will be bad, it is that I know that there are many diverse reasons to use benchmark-linked derivatives and a unique solution can not cover the majority of those reasons.

One important aspect of benchmark discontinuation is the disappearance of an underlying. If the previous strategy can not be attained anymore, i.e. there is no perfect replicating strategy anymore, you cannot reason in term of generally agreed value anymore. The standard  valuation of derivatives is based on replication strategy. There is no accepted common price without hedging strategy. If you remove the hedging strategy, the risk preference of each user is coming into play. No price compensation for the change of risk can be externally calculated anymore. We are back to the fundamental and evanescent price of risk! For each user, the price is what he estimates it is, not what an external party, even an independent expert, estimates. We may be able to set absolute bounds on that price, but no absolute exact value.

Transition from LIBOR, if required, will be extremely important. It will be costly (at the very least in time). Multiple solution will be designed and multiple solutions will be used.

Transition team

Who need to make proposal? As described below, ISDA is running some working group on new benchmarks and fallback. This will be a consensus opinion from the derivative industry. A similar working group is probably required from the end-users perspective. End-users form a  more diverse group. They will probably not be able to come to a consensus, but certainly they require to be informed of the implications and plan their strategy. Regulators are also running some working groups on the subject. Those regulators are usually finance industry regulators, the point of view of end users may or may not be in their scope. Maybe some consultation should be organised and the authors of contribution to the consultation invited to present their findings in a conference. Such a gathering, would probably not solved the question of a general agreement, but would certainly be an efficient way to expose the problems associated to benchmarks and benchmark changes, it would expose the different opinions and possible solutions.

Value destruction?

When I said earlier that there will be winners and losers, it is likely that there will be more losers than winners. As much as a willing transaction is in theory a win-win situation, an imposed new transaction — and a change of benchmark is a new transaction  — can be a lose-lose situation.

With new overnight benchmarks, replacement of LIBOR, new CSA reference rate, all trades under that CSA are economically changed: this is a lot of new trades and trade amendments Should they be treated as new trades from a regulatory margining and clearing rules perspective? To my opinion, the answer is yes. But maybe regulators, who are currently reviewing the coherence of the regulation put in place since the GFC, will take this opportunity to review the rules and change them in the direction of principle based regulation which would allow the decrease of risk and not rigid rule-based regulations.

The next transition

Planning for the dismissal of the next benchmark need to the prepared when trades referring to that benchmark are entered into, not when the benchmark is about to be discontinued. The design of the new benchmark cannot would not be complete without their fallback provisions. This would be similar in idea to the European Single Resolution Board (SRB). To my opinion, some of the SRB foundations are good ideas, at least the “R” planning part. As a believer in diversification, I’m not a fan of the “S” part nor of the associated fund, but this is a different subject. We now have a USD 300 trillion problem with the potential discontinuation of LIBOR; as much we need to deal with this problem now, as much we need to design a solution that does not simply kick the can down the road but contained the structural solution to avoid the repetition of a similar problem. A good fallback procedure, defined and accepted by the trade counterparts before the trades are entered into is necessary.


The UK reform group announced some month ago the support for a new SONIA, over other alternatives like RONIA and SONET. Among the arguments for that choice, one was that it is a better benchmark for the future “because it is use for discounting”. That argument is confusing the cause and the consequence. Sonia is used for discounting because of collateral remuneration; Sonia discounting is OIS discounting because the OISs use Sonia as reference; the collateral is remunerated at SONIA because it was the only benchmark rate available; it is the reference rate for OIS because it was the only rate available. The argument can be summarized by “SONIA is a better benchmark for the future because it was the only benchmark available in the past”. If we create a new index (RONIA, SONET or RIR), we have the possibility to change the market. Changing the market is difficult, as I have argued over the last years (see here and here), but possible. The difficulty of the change is a valid argument. But if that argument is used, it should be used explicitly, no hiding behind a pretense of risk free, reform or best practice.

Summary: The Working Group in charge of reference rate reform has decided to keep SONIA because it was the benchmark used in the past, i.e. the reform group has decided not the reform.

From an economical perspective, using a secure rate for collateral will always make more sense. The working groups for USD (SOFR) and CHF (SARON) have decided in that direction. This is a change with respect to current market practice. We will discover how difficult it is in practice over the coming years.

Fallback rate

With the FCA announcement of removing its support to LIBOR, the discussion about a potential fallback rate reform in ISDA master agreement have accelerated. ISDA has created a fallback committee that is working on proposals. The committee has already proposed some potential approaches to the fallback. At this stage those are only technical discussions, but we can expect that the final proposal will not be too far from those initial discussions.

One proposal would be to fallback LIBOR on OIS benchmarks plus a deterministic spread.

And OIS is the swap, not directly the overnight benchmark underlying it. A new benchmark would be created, based on the term swap, itself referencing the overnight benchmark. This would be adding an extra layer of rate benchmark: the benchmark is based on a derivative referencing the composition of another benchmark over a certain term. The OIS benchmark would need itself to be created. On what data would that benchmark be based? On some market players estimations, as the LIBOR and ISDAFIX, or on actual trades? If on estimates, how do we avoid the same manipulation risk than the one existing for LIBOR? If based on actual transaction, what is the reference data repository? Is it public and to which extend are the underlying trade details available?

Once you have dealt with the “OIS” part, you have to deal with the “spread” part. The idea would be to look at the market spread between OIS and LIBOR in a period before the discontinuation of the LIBOR. That spread would be recorded and applied unchanged for the remaining life of the existing LIBOR referencing trades. It will be a deterministic spread that would not be revised in the future, whatever what happen in the market after that date. It is not clear to me if the spread would be computed spot between LIBOR and OIS benchmark or on the full term structure of the rates, between LIBOR instrument calibrated curves and OIS calibrated curves. Using a spot spread would change the value of IRS significantly, repricing all of them from a forward spread to a spot spread; the difference can easily be 10s of basis points on some parts of the curve. Using the term structure of spread would require an acceptation of the way to compute the term structure of spread for the curve up to 50 years for each business day. Even leaving aside the question of the reference data (11:00 a.m. London, when LIBOR is fixed but the US market is barely open?), just the question of interpolation (see for example this blog or my multi-curve book) is enough to have also 10s of basis points for some dates. In any case, the question of the manipulation will still exist. If there has been manipulation in the past to gain a one day worth of fixing, what would be the incentive to manipulate if the gain is in one go for 50 years worth of fixing?

Suppose that we have solved all the problem of manipulation and methodology for the fixing of the spread. The spread is chosen to have (at best) the same valuation of swaps with standard collateral rules on the discontinuation date. But does that mean that all the other financial instruments related to LIBOR will have the same value on that date? The answer is clearly no. The spread will simply make the expected value (in the appropriate measure) of the LIBOR-linked coupons equal to the one of the OIS-linked coupons plus spread at that one date. Obviously the prices at other dates will be different (and LIBOR will not be observable anymore), but also the instruments that are not depending only of the expected value of the coupon will be different. This includes the swaptions, cap/floors, STIR futures, swap collateralized in a non-standard way, FRN, CMS, etc.

If we take the case of the CHF market, the current ON benchmark will cease to exist in December 2017, the replacement overnight index exists, it is SARON. To my knowledge no (liquid) OIS market on SARON yet exists. This means that the fallback method based on OIS benchmark would fail. Hopefully the market will start to exist at some stage, will become liquid enough in a couple of years so term OIS benchmarks (up to 12M) can be created. The same question will be relevant in the USD market when Effective Fed Fund Rate (EFFR) is replaced by SOFR. If there is not a liquid enough market by the time LIBOR is discontinued, we will need a fallback to the fallback.

The fallback methodology and data will need to the transparent, for each participant to decide if he want to enter into the standard fallback proposal or enter in a specific agreement with their counterparty. That may requires the full data set used for analysis to be made available without restriction to all interested parties, including end-users, academics, consultants and obviously private citizen. The same will be require for some code that implement the proposed methodologies, including full flexible multi-curve framework and curve calibration. Full term-structure interest rate model coherent with the multi-curve framework will also need to be made available to estimate the non-linear impacts of those spread changes. I’m currently researching on such models, but I don’t know any of them that fulfil all the requirements for such an analysis; the search is still on.

Once a fallback methodology has reached a (relative) consensus, what to do with it? Is it imposed to all users? In that case, I’m expecting multiple years of legal disputes. Is it proposed as a starting point of discussion? Is there also a methodology proposal to estimate the valuation impact of such changes? How is the inherent conflict of interest of market participant being part of the fallback committee and party in trades dealt with? Is the methodology validated by independent external expert? If yes, who is financing those experts? What is the involvement of regulator in choosing or imposing the methodology? The regulators have imposed clearing mandate for derivatives linked to some benchmarks and not to others. Is there a conflict of interest from the regulators regarding the future of those benchmarks? Can the clearing houses impose the fallback proposal to all their members and their clients? From a margining perspective, is the change of a fallback clause to a ISDA master agreement considered as generating new trades for all trades under that agreement? From an economic perspective, it is; from a regulatory perspective, an answer is required. How is the valuation of the trade for which the fallback methodology is not applied affected?

If OIS is a fallback for existing IRS with term reference rate. Do we propose also to have the OIS benchmark as the standard benchmark for IRS? Or do we want to change the market to a overnight only market. The choice of the OIS benchmark as IRS reference benchmark leaves the question of the robust OIS benchmark open. On the other side, the choice of a direct overnight benchmark means that the administrative burden of trading swaps is becoming more important. The reset has to be dealt with on a daily basis. Some IRS with corporates have today a fixing offset of one week, instead of the standard 2 business days, to give enough time to their administrative staff to deal with the reset. Is moving to a daily reset feasible for all of them? Are all the system ready to deal with composition of rates, or even worst, composition of rates with spread — ISDA standard definitions have 4 options for compounding methods.

Bank Credit

Some users may have used the LIBOR IRS, not as a hedge against level of rate, but as a hedge against banking sector term credit spread. In that case, the fallback to OIS or a repo based benchmark does not help; it would be better for them to have the trades cancelled. Should the fallback provision have some option for cancellation? Should the option for each trade be selected when the fallback changes are introduced or when the discontinuation is active?

Some variable mortgages are linked to LIBOR rates. This is very convenient for banks offering those mortgages as they have their assets and their liabilities linked to the same reference.

In Belgium, by rule, the variable mortgages are linked to Belgium government indices. This has lead in some cases to negative mortgage rates. But it also pushed the risk management issues in the hands of the professional lender, away from the responsibility of the private borrower. The private borrower does not suffer from the lost of credibility (credit spread) of the lender. As the mortgages are usually not marked-to-market in the bank balance sheet, the impact of the LIBOR-Government spread increase are unknown (to me). If LIBOR/EURIBOR was to disappear, this basis risk would appear not only in Belgian banks balance sheet but in many more balance sheets. How will banks deal with that risk when their borrowing costs (IBOR) is not present in vanilla IRS?

Initial Margin

When a new benchmark is created, obviously, no history for it exists. And it will take even more time to obtain an history of derivatives based on those benchmarks. The regulation related to mandatory Initial Margin (IM) call for historical VaR based on a 3-year history and “stressed periods”. Does that mean that the new derivatives have to be IMed with the scheduled based for at least 3-years and will need to wait for a significantly stressed period? Many other models and regulation based on historical estimates will need to be reviewed or adapted to those new situations.


Questions, questions, I have questions. Some call me question Marc! Why?

If you have answers or more questions on the Game of Benchmarks transition, don’t hesitate to contact me — through the comments of this blog or privately.

Maybe we can organize a Game of Benchmarks conference. 

Season 1

Episode 1: The king is dying.

Episode 2: Nobody is running for the throne.

Episode 3: The great pretender.

Episode 4: Transition and transition team.

Episode 5: The court. (forthcoming)



AD in finance - endorsement - Luca Capriotti

I had the honor of having my new book endorsed by experts on Algorithmic Differentiation. The endorsement can also be found on the book's back cover.

(Adjoint) Algorithmic Differentiation has quickly become an indispensable tool in modern financial engineering. Marc Henrard’s book is a lucid and concise introduction to the topic. The subject is introduced simply and clearly, from a mathematician’s prospective, and with the clear intention of demystifying the `black magic’ behind the staggering computational benefits of the technique. A nice read that many practitioners are likely to find useful.

Luca Capriotti
Visiting Professor
Department of Mathematics, University College London


More EUR adjustments?

The ECB has decided to published a new unsecured overnight interest rate benchmark. The press released was posted on its website a couple of days ago. No name has been proposed yet for the new benchmark.

This would be a new benchmark on top of the existing EONIA and STOXX GC Pooling Index.
Those two benchmarks are already the underlying of some derivatives. It is expected that the new index, planned to be published by 2020, will also be used in some derivatives.

That would mean three competing overnight benchmarks in EUR all of them with associated derivatives. That would means twelve (12) possible ON derivatives types. One type for each of the benchmarks used as underlying in combination with each of the benchmarks used for the computation of interest on the mandatory VM amounts, to which you have to add futures, which are equivalent to derivatives with a collateral rate of 0. And you have to add the potential difference in capital treatment for the settle-to-market feature.

The multi-curve framework is definitively not dead, even if LIBOR is dying. Interest rate modelling will continue to be extremely important for all financial markets users. Even if the so-called exotic derivatives have decreased in important since the crisis, the modelling techniques developed for them are becoming more an more important.

I'm working on different research works related to the modelling of the potential impact of the LIBOR disappearance. I will probably take another couple of months to have publishable results, but certainly the changes in the market continue to provide material for academic research and advisory business. Don't hesitate to contact me about any of them.

AD in finance - endorsement - Uwe Naumann

I had the honor of having my new book endorsed by experts on Algorithmic Differentiation. The endorsement can also be found on the book's back cover.

With the number of Greeks relevant for the robust evaluation of financial products increasing steadily over recent years the subject of Algorithmic Differentiation has been gaining substantial popularity in computational finance. Marc Henrard presents an accessible explanation of the subject from the perspective of a highly experienced developer of financial simulation code. His book establishes a very useful entry point into the exciting world of adjoint methods in finance for both practitioners and academics.

Uwe Naumann
RWTH Aachen University


AD in finance - endorsement - Andrea Macrina

I had the honor of having my new book endorsed by experts on Algorithmic Differentiation. The endorsement can also be found on the book's back cover.

An easy, short and smooth path to Algorithmic Differentiation in Finance!

Andrea Macrina
Reader in Mathematics
Department of Mathematics
University College London



The printed copies of my book

Algorithmic Differentiation in Finance Explained

are now available.

Picture of the book with Canary Wharf in the background.


Settle-to-market: a quant perspective

Following recent regulatory guidance in the US, announcement by Barclays that it had reduced its regulatory assets by USD 113 billions, and last year switch by UBS that saved USD 300 millions in capital, I though it would be useful to give it a quant perspective to the settle-to-market question.

The centre of the question is to know if the VM mechanism in cleared derivatives is a “settle-to-market” or a “collateral” process. This is only a wording question, but what is the quantitative finance perspective? In both cases, the valuation fall in the generalised collateral framework. I use my “Multi-Curve Framework with Collateral” paper from 2013 as a representative example of that framework (also described in my multi-curve framework book). It’s starting point is, in all cases,

The price process is constant at 0. That is a perfect example of settle-to-market. The continuous dividend/pay-off is a mixture of change of value dVt and payment linked to a benchmark ct Vt dt. The number is called rate, but in all generality it is a reference number, nothing else. In some cases it is a rate (like overnight) it some case it is a conventional number (0 for futures).

Citing the great Poincaré, as I did just below the above definition in the paper,
La mathématique est l'art de donner le même nom à des choses différentes. 
Henri Poincaré.

Most derivatives,  cleared or uncleared, are now traded under mandatory daily VM process. If we ignore the wording and concentrate on the content, all of them fall in the settle-to-market category in the above sense. If you thing that names are more important than substance, just rewrite your contracts. Instead of a vanilla interest rate swap, call it ‘path dependent multi-index contingent claim with daily pay-off’, write the above formula in the term sheet, make sure that you write explicitly in the contract that the value is settled-to-market on a daily basis and the residual value is exactly 0 on a daily basis, settle the daily pay-off in cash and you are done. You can use the settled-to-market term for all your derivatives.

Obviously, this is a quant perspective, not an accounting or regulatory one. But hopefully there is only one reality. Hopefully also the common sense perspective that two assets that have exactly the same pay-offs in all circumstances are equals is true not only from a quant perspective, but also an accounting or regulatory one.
Who would you give different names at the same concept?


The future of LIBOR: some articles

Many articles have been published recently about what could happen to the interest rate market if LIBOR is discontinued or at least is not the main rate benchmark anymore.

A list of some of those articles is provided below, in no particular order. I link to those articles because I believe it is important to have an open discussion about the subject. It does not mean that I agree with everything that is written in those articles.

Don't hesitate to add more references in the comments.


Game of Benchmarks: Season 1 - Episode 3: The great pretender.

What are the qualities required from an interest rate benchmark? What would a great pretender to the benchmark throne look like?

The qualities should include (in no particular order)
    •    Un-manipulable
    •    Observable
    •    Tradable
    •    Relevant
    •    Transparent


This does not need a lot of explanation. If you have to pay for something, you don’t want that a someone else is able to decide how much you have to pay without your say.


By opposition to a random number, the benchmark should be based on real economically meaningful items that can be observed by the general public and not only the benchmark administrator. A guess by a self-selected group of benchmark setter, is not an acceptable approach. The best would be to base the benchmark on public information. But there is only a limited amount of public information available in a timely manner in finance. Nobody want to disclose in real time all its transactions. If the benchmark is based on actual transactions, it will probably be difficult to have it really observable.


It should be relevant, not only as an economical abstraction, but as a reality for the users. This is very difficult, as there are two parties in a contract, but here I will take the point of view of the end user, the retail borrower, the corporate, etc. Why would an interbank borrowing rate be relevant to a retail mortgage? For a very specific bank worker, it may be the case as his bonus is linked to the profitability of the bank which itself is negatively correlated with the interbank credit spread. For him, a reverse LIBOR spread mortgage may make sense. But beyond that far-fetched example, it is difficult to see why a retail mortgage would be linked to LIBOR. Similar remarks could be made for municipalities borrowing at rates linked to LIBOR or ICE swap rates (formerly ISDAFIX). See also the ’term’ section below.


It should be possible to trade the benchmark underlying directly, not only derivatives on the benchmark. If we take today’s LIBOR, you can trade futures on LIBOR 3M, but you can not trade the numbers used in the benchmark calculation. The numbers are abstract items existing only in the head of the rate setters, you cannot trade the neurons of the rate setters. An alternative approach would be to let the futures trade up to 11:00am and use the last traded futures price, not only as a settlement price for futures, but also as the fixing for the LIBOR. The LIBOR so determined would be used in other derivatives like swaps. This method of fixing as certainly many drawbacks, that I don’t want to consider here, I just want to point one advantage: the benchmark is directly tradable. You can hedge the fixing and you can influence it, in the economical sense, by trading the future. I have done a similar proposal a couple of years ago for deliverable swap futures where the last settlement price would be used as a fixing for an index used in CMS-like products. In that manner, you need less additional compliance mechanism, the market is your compliance department.


The benchmark should be based on information that are public, with clear rules that can be checked by external parties, not only the benchmark administrator.

I will include also under the ‘transparent’ qualification an element that I have not seen in other places. The benchmark itself should be public information; the numbers should be made public as soon as known, no license or fee should be required to obtain the number. Any analysis, of current data or historical data can be run by all interested parties, including any party in a trade, academics, regulators, etc. All the data used for the computation of the benchmark should be fully public as soon as known, no delay in the publication is allowed. Allowing a license/patent/fee on benchmarks used by retail (I’m not speaking here of the interbank market, where professionals are on an equal footing and free to chose their weapons), is creating an undue legal protection to block the fair assessment of the situation.

In my definition of transparency above, I see a clash between free enterprise and freedom to inform. LIBOR values should be considered as news, not proprietary corporate secret. Full access to the data should be granted to all. Maybe this requirement could appear in some retail consumer protection requirement: if a retail product is linked to a benchmark, full transparency and access to data by all is required for that benchmark. For systematic benchmarks, data access should be granted to researchers (academic, independent) for public research on them. No patent can be declared on news, truth and formulas. The benchmark values should be considered as news. Academics and regulators — and in general any researcher — should be free to develop analysis, including writing code, of the benchmark and publish their results about it, including the code, the data, their findings and their opinions.


What do we need a benchmark for? For saving time in lending activities and related derivatives. Most of the lending is done for a term, i.e. the borrowing is planned to be reimbursed at a agreed date. Credit lines are different, but do not represent the majority of the borrowing activity. Most of the lending is for a period longer than a single day. The alternative rates that have been presented are all overnight based. In that sense they all fail to be relevant for most mortgage and corporate lending. I would prefer to have one of the new benchmarks related to term rates, like 3-month or 6-month rate, rather than all of them overnight.

Risk free? 

Some discussion about the alternative rates mention ‘risk free rates’. It is in particular the case of the Bank of England sponsored Working Group on Sterling Risk-Free Reference Rates. Why do we need a risk free rate when risk-free activities, like risk-free money lending, do not exist? It is useful to have a reference rate. LIBOR was a reference rate. The fact that its design was bad and opened the door to obvious manipulation does not remove the fact that it was a reference rate and it that sense did a good job for 30 years. We want to change it, fine for me. The first question is, what is the target. Certainly a risk-free rate is of no practical use to anybody in practice and miss all the above qualities. Can a practical benchmark be created on a risk-free rate? Another question altogether. To my opinion the answer has to be 'no'; risk-free rate is a theoretical concept, you would need a theory to compute it from practical measurements. Then someone else will need a potentially different theory to compute, from the reference risk-free rate, anything he wants to use in practice. I don't see any interest in there.

I confess I have used risk-free rates in theoretical development. But only as an intermediary step, as a guide to intuition. No final formula or price never depended on knowing it or estimating it.


Do we want a unique benchmark to dominate all of them, like the old king? Or several specific benchmarks? The first quality I mentioned was relevant. This implicitly mean multiple benchmarks. This will also mean that the multi-curve framework is here to stay ;)

In a comment to a previous blog, a reader asked about multiple fixing for same benchmark at different time of the day. I understand that this can be handy for professionals to have a fixing at a time which is convenient, like the time they revalue their books. But from a end user perspective, I’m not sure it make really sense. If my mortgage rate is fixed once a year, I don’t really care if it is done at 11:00am or 3:00pm. Also multiplying the fixing time would multiply the derivative underlyings. Do we really want to create a basis swap market between LIBOR 3M 11:00am and LIBOR 3M 3:00pm? I would prefer not.

Season 1

Episode 1: The king is dying.

Episode 2: Nobody is running for the throne.

Episode 3: The great pretender.

Episode 4: Transition and transition team.

Episode 5: The court. (forthcoming)


Game of Benchmarks: Season 1 - Episode 2: Nobody is running for the throne.

What are the alternatives to LIBOR?


Sensu stricto: none! LIBOR is a measure of the interbank unsecured lending rates between London banks in different currencies. The reason why the LIBOR benchmarks are replaced, beyond the past history of manipulation, is that the interbank unsecured lending has reduced dramatically. The reduction has reached such an extend that some of the indices do not really make sense anymore. The indices measure daily the average rate experienced by multiple banks for borrowing from their peers at a single point of time (11:00 am). In some cases, the mechanism that is measured take place only once a week or less. If no tree falls in the forest and everybody is listening intently, how do you best describe the average sound? There is almost no way to create a new interbank index due to the lack of underlying market. To the best of my knowledge, nobody is actually trying to propose an alternative interbank term benchmark.

In some sense you could argue that using transaction based fixing would be easier to manipulate than the current mechanism. If there are less transactions than rate setter, it would be easier to agree a (small) transaction at a suitable rate with one person which will be the base of the fixing than to collude with enough rate setters to move the market significantly.

What are the proposed indices?


Different new indices have been proposed recently. All of them are of the overnight type. The indices that have been discussed recently are: SARON (CHF), BFTR (USD), SONIA (GBP). The SARON index is a repo based index that has been indicated to replace the CHF TOIS. The relevant committee has indicated that the replacement will be finalized by year end. As expressed earlier, I have my doubts that the replacement can be fully effective in a so short period of time. For SONIA, this is not a new index, but an adaptation of an existing index. For the USD, the BRTR is based on repo rates. The index will start to be published in 2018. The rate has been selected by the Alternative Reference Rate Committee (ARRC).

All those indices are of the overnight type, this means that they can not replace directly LIBOR which is used mainly in its term deposit versions, with the most used terms being 1M, 3M and 6M.

I have read in a lot of places the suggestion to replace LIBOR by “OIS”. I have to confess that I don’t understand what that actually means. LIBOR is a term deposit benchmark while OIS is a derivative. Does that mean that OIS is understood as its actual meaning of a swap and instead of using a 3M deposit benchmark to fix the rate on a quarterly basis, a 3M OIS benchmark would be used instead? In that case, the ON benchmark is not enough. You need an extra layer of OIS benchmark, which itself refers to the overnight benchmark, with the similar questions on how to derive such a benchmark. The historical IRS benchmarks, like ISDA FIX, used in CMS-like products, have also been accused of manipulation over the recent years. Is the propose replacement by OIS a misnomer and should be read as replacement by overnight benchmark? In that case the benchmark is readily available, but how do you apply a daily benchmark to a quarterly fixing? Do you change the fixing frequency to daily, with all the back-office, risk management and valuation impacts? Do you keep a term fixing with the overnight rate, with the risk management and convexity adjustment impacts?

I will discuss more of these issues in the next episode, “the great pretender”, where I will describe what I thing should be the required features of replacement benchmarks.

ICE appear to be willing to continue with the LIBOR benchmarks, even without the support of the FCA. So there may be a LIBOR after 2021. If this is the case, there will be no forced transition by that date. It will leave more flexibility for the user to do the transition or not and if yes, when to do it.

Where is the throne?

I titled this episode “nobody is running for the throne”, but I have never said what the throne is! We know who is on the throne today: LIBOR. We know who LIBOR is, an interbank rate. But it is not because today we have one unique ruler of a “united kingdom” of interest rate, that the best strategy is a unique ruler or that the ruler has to come from the same familly. There is the interbank market, there is the government market, there is the secured/collateralised/repo market, there is the corporate market with all its sectors, there is the retail mortgage market, and so on. All of them deserve a specific benchmark. This may lead to a fragmented (derivative) market, with plenty of basis, but it is how the reality is. One of the roles of the banking system is to offer risk management services to the users. In last 30 years, the final users have borne the basis risk between the interbank market and their actual risk; maybe it should be reverted to its natural order and the banking system should offer that risk management service to the market in general. This would also mean that banks should be allowed to keep (some of) that risk in their books, run open positions, and be remunerated for it. You cannot do that at large scale without reviewing all the regulations about market risk and capital. Are the current regulation viable if the new benchmarks are introduced and the banking system is in the business of managing (and taking) market and credit risk? A reform of the benchmarks may require other reforms? Can it be that with new benchmarks in place almost everything is becoming a non-modellable risk?

The throne and the court

The pretender to the throne is not the only thing that need to be sorted out. The full court will need to be reviewed. This consists in a long list of swaps, futures, options, collateral remuneration, etc. that rely on the benchmarks. The new products will need to be designed. The design has to take into account the business, risk management and quantitative finance aspects of those products. Luckily, the well design products to match business and risk management requirements have often a simpler quantitative finance impact. The design of those products is worth a forthcoming episode on its own. A nice name for the episode will be “The court”.

In the waiting of its publication and for implementation details don’t hesitate to contact me for advisory work around those products. Some of my recent designs include options on futures bundles (presented 18 months before CME launch), rate based deliverable swap futures (not launched yet) and cap/floor on compounded rates.

Season 1

Episode 1: The king is dying.

Episode 2: Nobody is running for the throne.

Episode 3: The great pretender.

Episode 4: Transition and transition team.

Episode 5: The court. (forthcoming)


Multi-curve framework: 10Y at the fore

The first section of my multi-curve framework book is called 9 August 2007. The reason for using such a title for the first section can be visualized in the book's Figure 1.1; the interest rate derivatives world changed on that day.

Today it has been 10 years since that day.


Game of Benchmarks: Season 1 - Episode 1: The king is dying.

Over the last years, I have reported different initiatives around the changes of benchmark interest rate indices.

With the announced death of Libor recently accelerated by FCA’s CEO, it is probably a good time to discuss what a good index would be and how the replacement of the current indices could take place.

I will present my opinion and suggestions regarding the interest rate benchmarks in a series of blog. Several episode are in the making, and certainly more than one season will be required before the drama unfold fully! The script of the next seasons still has to be written, by the current readers maybe.

The series is titled

Game of Benchmarks.

Game of Benchmarks: a no-fantasy series with no blood and no sex but plenty of greed, manipulation and money.

Season 1 - Episode 1: The king is dying.

The most important number in the world that nobody knew existed — The king is dying — Where is the successor?

The most important number in the world!

LIBOR has been called “the most important number in the world”. It was widely known by this nickname only well passed its prime, when people started to question its significance in the wake of the Global Financial Crisis.

Why is it the most important number in the world?

Before explaining why it is important, I have to explain it is a number. It is a number in the literal sense, i.e. an arithmetical value, not a physical measure. For human kind, some measures are more important than the LIBOR number(s), like the temperature at the Earth surface. LIBOR is simply a number, an abstract quantity, from which some economical consequences, like the rate on loan or derivatives, are derived — “derived” and “derivatives” have the same root. By definition (1), LIBOR is at its core not a measurement or a economical reality, it is part of the imagination of a small number of “rate setters”. It is not a reality but a guess by someone about what someone else would offer him(2).

The number was at the start an internal convenience created by an association (British Banker Association - BBA) for the benefit of its members. Since, it had a dazzling career that brought it to royalty or maybe even to “imperium”, as it reigned not on a mere kingdom but on the world. How did this local man became a global force? With the help of men in power. Obviously, the bankers helped it on its ascent, this is expected and fair as it was their creature. But it was also helped, intentionally or not, by regulators, lawmakers and central bankers. Each time one of those public servants referred to it in regulation, law or analysis, it gave it more power. Soon LIBOR took over the world, not only for derivatives and interbank agreements, but also for almost everything linked to interest rates: retail mortgages, corporate lending, economic assessment, central bank policies, etc. Not that the LIBOR was the best number for any of those tasks, only that it was the only one available and nobody beyond its creators questioned it. It ascended to the thrones not on its own strength but from the support and ignorance of men in power.

The interest rate market is, by far, the most active asset class, well above equities or commodities. The traded notional of interest rate products is well above the amount of equities. Even if equity indices (like S&P 500, Nasdaq 100 and Eurostoxx) are attracting more news coverage, it is not where most of the activity of the financial markets take place. As a number, USD-LIBOR-3M is more important than SPX or SX5E.

The “L” in LIBOR stands for London and the first “B” in BBA for British, nevertheless the numbers have a worldwide impact. The reason is that the benchmarks are publish in many currencies — originally 10 and only 5 since 2012 (3)— and in particular in the dominant currency in the financial markets, the USD. The British Empire still survives, just not where you expected it. It has always been a surprise for me that the US market has accepted to trade most of its interest rate market based on an number coming from abroad and decided while they sleep (LIBOR is set at 11:00 am London time, which is most of the time 6:00am New York).

It is important to keep that history in mind, not to put the blame on the actors of the past, but to design a brighter future. To create a new benchmark, you have to be clear why you need it, how it will be used and what features you want from him.

Why do we need benchmark indices?

The quick answer is: to save time. There are many circumstances where financial processes need to be repeated frequently by many people. For example you want to borrow money on a daily basis to manage the inventory of your shop. You borrow short term (overnight) and many shops like yours do the same. You have the choice, either every day you go to the bank and discuss with your account manager, who himself has to check with its treasurer, to agree on a rate, or you agree a reference figure that will be used for all your borrowings. The reference should not be set by one of the parties, or someone who has a conflict of interest with the parties. The best is to have as a reference a number which is a publicly available information proposed by a trusted third party source.

The LIBOR started in that way to simplify the management of syndicated loans. Banks submitted their rates to their own association which was redistributing it to its members. There was no conflict of interest, or more exactly all the participants had the same conflict of interest and the same power. Then the indices were used in other circumstances that are somehow financially similar. The benchmarks were used in interest rate swaps — interbank or not —, for corporate bonds, commercial mortgages, retail mortgages, the remuneration of collateral, etc.

We need benchmark indices for convenience. But do we need one with imperium, like LIBOR is? Not really, we could continue to have LIBOR for interbank lending, some repo based benchmark for secure lending, some government bond benchmark and probably others. But I have to warn you already, if you have not read yet my book on the multi-curve framework — but I cannot imagine that to be the case —, each time you add a benchmark rate somewhere, your valuation framework is becoming more complex. Maybe you don’t care about valuation framework as you are not a bank, but that would be a mistake. More complex valuation framework means more difficult accounting for banks and corporate, disputes and trials to resolve them, difficulty to rescind contracts even amicably, more regulation, etc. It means unnecessary costs that in fine are paid by the end consumers, i.e. you, my dear reader. Human kind need to produce more food and shelter so that some of the members of the species (me in particular) can deal with the minutiae of multi-curve valuation and disputes around it.

More elements regarding the requirements of a good benchmark will be discussed in Episode 3: The Great Pretender.

We need benchmarks, probably several of them, but not too many of them either.

What are the other indices similar to LIBOR?

There are certainly a number of other benchmarks that play a role similar to the role LIBOR plays in USD, GBP, JPY and CHF (and EUR). Some of the other benchmarks, also based on interbank lending are: EURIBOR (EUR), CIBOR (DKK), HIBOR (HKD), TIBOR (JPY). In EUR, the EUR-LIBOR exists and replaced the pre-euro FRF, DEM, BEF and other LIBORs. But most (or perhaps even all) of the new instruments in EUR are linked to EUR-EURIBOR, and only the legacy trades to EUR-LIBOR. In JPY, a large portion of the market is in JPY-LIBOR, but an active market exists in JPY-TIBOR. There is even two versions of TIBOR, a domestic one and a euro-JPY one.

Other benchmarks play a similar role but are not based on interbank lending. In AUS, the leading Benchmark is BBSW, based on bank bills and in CAD the benchmark is CDOR based on bankers' acceptances.

There are other types of benchmarks that are very important but play a slightly different role. They are the overnight indices. They are usually computed as the weighted average of the rates on actual trades. They are more than “numbers”, they are the measurement of an actual economic reality. The best known are  Fed Fund effective (USD), EONIA (EUR)  and SONIA (GBP)

But none of those indices are real pretender to replace the LIBOR. In the next episode, I will review why it is so.

Summary: The previous king is dying, from his own fault — manipulation — and from the same causes that brought it to the thrones — used where it shouldn’t have. For convenience, one or several successors would be very useful. No great pretender to the thrones as of yet.

Next episode:
Game of Benchmarks. Episode 2: Nobody is running for the throne.

(1) The exact question ask to the LIBOR rate setters is: “At what rate could you borrow funds, were you to do so by asking for and then accepting interbank offers in a reasonable market size just prior to 11 am London time?” See the ICE LIBOR page.
(2) EURIBOR has even one extra level of guessing, as it is the rate at  "which euro interbank term deposits are offered by one prime bank to another”. Each panelist has to guess what the other panelists’ banks will ask each other.
(3) See the Interest Rate Instruments and market conventions guide

Season 1

Episode 1: The king is dying.

Episode 2: Nobody is running for the throne.

Episode 3: The great pretender.

Episode 4: Transition and transition team.

Episode 5: The court. (forthcoming)



LIBOR is dead, the Game of Thrones can start!

Today, Andrew Bailey, chief executive of the FCA, delivered a speech related to the future of LIBOR - not to futures on LIBOR ;)

The main message was that the FCA will support LIBOR up to 2021 but not beyond and encourage the market to start the transition to alternatives today.

Ending the publication of LIBOR by 2021 may be possible. Replacing it in earnest by something else by that date is a completely different task. Swaps have maturities up to 50Y; if you stop publishing LIBOR, parties to the contracts have to use the fall back in the contracts. If you want to replace LIBOR by one new benchmark, you need the agreement of all the parties involved, it means each party to each and every single contract referencing LIBOR has to agree individually. There seems to be an agreement with this in the terms of the speech. I was happy to see that the terms "challenging " and "extremely difficult" were used in relation to the change of benchmark.

Even if the "L" in LIBOR means London and LIBOR is the king of indices, LIBOR is not an hereditary monarchy.
The King is dead, long live The King!
is not a proclamation that is appropriate. I would say
The King is dead, the Game of Thrones can start.


Book's title

Another look at my forthcoming book cover: the book's title.

Book's spine

A first look at my forthcoming book cover: the book's spine.

Change of benchmarks and margin regulation

As discussed six months ago in my blogs (here and here), new benchmark indices mean new trades, new trades mean mandatory margin.

If the interest rate benchmark indices like LIBOR, EURIBOR, SONIA, Fed Fund Effective or TOIS are modified or replaced, the contracts referencing them need to be adapted. Those contracts include the CSA referencing those indices as interest rate for cash collateral. Each contract need to be modified individually after agreement of each of the parties in the contract. If a contract is modified, it is considered as a new trade for the regulation related to mandatory margin. For all new trades, a mandatory daily Variation Margin (VM) applies for all counterparties and mandatory segregated Initial Margin (IM) applies for large derivative users, with more and more users falling in that category over time.

The logic of the consequence of reorganizing the market infrastructure for benchmarks seems to have finally reached the "lawyers". A recent article in Risk details the opinions of different lawyers working in the financial market on the subject. Even if it is presented as a new discovery in the article and in round-tables, it is nothing new for you, my blog's readers. Remember my February blog where I said "Don't underestimate this issue" when I discussed the replacement of TOIS by SARON. According to the Risk article, the question was also asked earlier this month at a Bank of England-sponsored round-table related to the reference rate reform. Maybe by someone who had read my earlier blog.

To my opinion, the impact is not only on contracts mentioning the rate index directly but also on contracts referencing it indirectly through the CSA. For example if an equity derivative contract was referencing a CSA with the possibility to post collateral in CHF cash with payment of interest at TOIS, the replacement in the CSA of TOIS by SARON would clearly be a new contract. Under the spirit of the regulation, that equity contract will fall under the mandatory margin regulation. I have not heard any official opinion on this point of indirect impacts.

The rule is clear: any new trade will fall under the mandatory margin rule. Clearly a trade with a new benchmark index can only be a new trade. I have my personal disagreement with the way the rules have been set-up, e.g. expressed in my answer to the EBA request for comments in July 2015, but certainly I support a clear rule that is applied without exception.

Mentioning that the new contracts are "unintended consequences" of the change of benchmark is not an argument. First I hope that regulators and lawmakers have thought about all potential consequences before proposing a rule and that none as obvious as the one discussed here would be called "unintended". Second, if "undesired" consequences were a valid argument, there are plenty of earlier cases were it should apply. For example when doing compression of bilateral portfolios you would be allowed to use vanilla swaps, even if they are mandatory cleared for some users, without having to use synthetic derivatives (see the Risk article on the subject). Also multilateral netting of IM would be allowed if they decrease systemic risk.

Why do I, as a quant, care or give my opinion about legal matters? The legal framework of derivative contracts is now a sub-discipline of quantitative finance; the valuation of derivatives includes the exact wording of the term sheets and applicable regulation. Quants have the most complete view on the pricing, including the impacts of exact contract and regulation wording. The quant community opinion on this matter is at least as important as the one of the legal community, actually more important as they can quantify the impact, not only acknowledge its existence.

I'm curious to see what will happen in case of change of benchmark indices, in particular in the CHF market with the planned discontinuation of the TOIS and the creation of the new SARON. How much issues will it create on the derivatives referencing TOIS directly? How much issues will it create indirectly through CSA referencing TOIS?

Without a doubt a subject TO BE CONTINUED in another blog.


Libraries - censor - controversial

[...] libraries should be open to all—except the censor. We must know all the facts and hear all the alternatives and listen to all the criticisms. Let us welcome controversial books and controversial authors.
John F. Kennedy
29 October 1960


Collateral Square

I first discussed collateral square in my 2013 paper Multi-Curve Framework with Collateral. The name collateral square itself had been suggested by Damiano Brigo during discussion on the paper first draft. To my knowledge, the theory behind the pricing of derivatives collateralised by assets that can themselves be repoed was first described in the above paper. It is also described in my multi-curve framework book.

The origin of the term "collateral square", which reminds the CDO square terminology, is that the bonds are provided as collateral to the derivative and then the bond is provided a second time as collateral to obtain the required cash; the collateral to the derivative is provided as collateral to a term deposit.

A recent article in Risk, titled The price is still wrong: banks tackle bond CSA discounting, describes the recent evolution in the EUR market in which the ON repo rates (for high quality bonds) are well below the EONIA rate, up to 40bps and even several percent at quarter end.

As often the case when there is a discussion about collateral and discounting, I would like add some personal comments and analysis.

In general, to price collateralized derivatives, the "discounting" is done using the "collateral rate". The discounting is done using the overnight rate - or overnight repo rate of the asset in case of asset collateral - cash account. It is only in exceptional circumstances that the overnight compounded of the cash account can be transformed into an actual know long term discount factor. This very special circumstance is realized in the main currencies for the overnight main indices through the OIS market. As this special case is the standard for all the main currencies, one tends to forget it is an exceptional circumstance; my dislike of the term "OIS discounting" and regular rants about potential changes in the related markets comes from the use of a common place name for an exceptional circumstance. The OIS market transforms a compounded overnight into a fixed rate over a potentially long period. Overnight rate discounting can be transform into OIS discounting by a change of numeraire, and the market provides us a practical tool to realize the change of numeraire!

The article mentions the long term repo rate that would be used (after change of numeraire) to discount the long term derivatives cash-flows. What the article does not mention is how to transform the ON compounded repo rate into a long term repo rate in the market. This can be achieved in the following way: Receive the bond in a long term repo transaction in which you provide the cash for a long term and received the associated long term repo rate. At the same time, repo out the bond overnight, receive the cash overnight and pay the overnight repo rate. This look theoretically, from a derivative pricing perspective, like the OIS case, transforming an overnight rate into a long term rate. The first big difference, often mentioned, is the absence of long term repo market. The second big difference, less mentioned, is the balance sheet impact of the repo transformations. As I mentioned in one of my previous blog, I have grown-up from a derivative quant to a balance sheet quant; before using a pricing formula I have to look at how to implement the hedging strategy (derivative quant) and its impact on balance sheet (balance sheet quant). To realise the EONIA overnight to long term transformation, a single clearable and balance sheet cheap OIS is enough. For the repos, the transformation involving a repo and a reverse repo described above is required. The cost in term of capital to put those two transactions in place is a lot higher than the OIS; probably nobody would enter is such a costly hedging scheme only to hedge the discounting risk.

In term of pricing a new ATM vanilla IRS, what is the impact of the cash v bond collateral, i.e. overnight EONIA v overnight repo discounting? Personally I have no way to estimate the exact difference. It would require to estimate the convexity adjustment between the EURIBOR forward rate under EONIA discounting and repo discounting. Remember what the forward rate is. It is not a economic quantity that is measured on its own, it is the number to be put in a old formula to obtain the right price (Definition 2.1 in my multi-curve framework book). The forward is defined from the price, not the opposite. You cannot compute the price in a new circumstance from a forward rate estimated somewhere else without theoretically justified adjustments. This requires a three curves model for EONIA, ON repo and EURIBOR, including all the co-dependence (correlation) between them. Moreover, there is no way to hedge any of the model risk generated by those multi-factor model, due to the absence of liquid market. If I have to market make a swap book and I'm asked to quote a bond collateralized swap, my only protection is a large bid/offer spread. I can compute my PV01 risk with respect to EURIBOR collateralized at EONIA, EURIBOR collateralized with bonds, the associated discounting, but I don't have liquid hedging instruments. My strategy would be to try to balance the book with other bond collateralized IR derivatives and take a large bid/offer spread protection when quoting those trades to be able to survived unhedged market movements.

The article seems to indicate that banks have ignored the difference between bond collateral and cash collateral in part "because there is no liquid term-repo market that can be used to accurately price long-dated trades". As a former swap trader, this would be a supplementary reason for me to take it into account! If there is no way to accurately price and hedge the trade, that is where I would put more risk management and pricing efforts, not less. I may use OIS levels to estimate the shape of the long term repo curve, but I will certainly have a specific repo curve and spend a good amount of time analyzing the non-hedgable model risk of that curve.

Now if we ignore the known unknown that the convexity adjustment between forward rates is, what would be the change of ATM rate for a vanilla EURIBOR IRS? Currently the repo rates are lower than the EONIA rates and the EUR curves are upward sloping. The curve being upward sloping, this means that in a receiver IRS, on the short term part of the IRS we will receive a net cash flow (fixed higher than forward) and on the long term part of the IRS we will pay a net cash flow (fixed lower than forward). Discounting at a lower rate is increasing the value of all the cash flows but the impact is larger on the longer term. The impact is higher where we net pay; the IRS with the same fixed coupon has less value. To obtain a fair ATM IRS, the fixed coupon received has to be increased. In summary, given the current upward shape and negative repo spread, ignoring convexity adjustments, the IRS should have a higher fixed coupon for bond collateral.

When trading IRS with clients under a symmetrical bond-only CSA, the banks will receive and post collateral, depending of the market movements. The higher cost of collateral is potentially in both directions, it is not necessarily a gain for the bank; it is no "keeping the benefit", it is "keeping the risk", positive of negative. But this is fair, one of the raison d'être of banks is to manage financial risks, not to avoid them. Probably certain categories of clients have a derivative portfolio which is mainly made of receiver swaps. Feigning of ignoring the impact of bond-only collateral will allow to underpay the fixed rate as described above. But once that initial mis-pricing has been realized, during the life of the trade, the spread can generate a monetary gain or loss; but what is certain is that dealing with the repo market to align the trade arrangements to the main liquid market based on cash collateral will be a cost in term of operation and balance sheet. For that part it is "keeping the cost".

The Risk article also repeats the traditional view that OIS discounting appeared in 2007 following the divergence between EURIBOR and OIS. There has always been a decently large spread between EURIBOR and OIS, even before the crisis. Before the crisis, the spread was lower and more stable at around 10 to 12 bps. Moreover the OIS discounting, even if under a different name and with less theoretical developments than today, as been used well before the August 2007 start of spread volatility. I have used similar technique for trading as early as 2004 or 2005 and my first 'irony' article was published in Wilmott magazine in July 2007, before the start of the crisis.

An interesting question that could be asked, is the potential for a segmented market with a bond-only collateral market developing in parallel to the main cash collateral market. Part of the answer could be present in the potential move by Totem to start benchmarking that segment. The market segmentation of bilateral trades has to be put in parallel with the segmentation of the cleared market, e.g. the existence of a LCH v EUREX spread in EUR IRS. The spread exists not necessarily for fundamental difference between the economics of each market, but because of the difficulty to cross the markets. The regulations, balance sheet constraints and market infrastructures are creating barriers in a global market. Could it be that the world is becoming geographically global but local in term of classes, not social classes but market infrastructure classes?


Further news regarding Alternative Reference Rates

A couple of days ago, the US Alternative Reference Rates Committee has published an announcement regarding its "preferred alternative reference rate". The announcement can be found on the New York fed web site at https://www.newyorkfed.org/arrc/announcements.html.

The proposed rate is based on repo transactions. It is certainly a useful new benchmark and a useful reference for "new USD derivatives". A discussed previously in this blog in post on similar subjects, and as implied by the name of the committee, this is an alternative reference rate, not a replacement of the LIBOR rate. The repo rates have a different credit implication than the inter-bank transactions underlying LIBOR. The risk management and valuation features of the two benchmarks will be different. The new benchmark will lead to "certain new U.S. dollar derivatives". Implicitly, this means also new markets, new clearing infrastructure, and new master agreements and CSAs.

The alternative benchmark is only proposed at this stage; it is not yet finalized and not yet published. Consequently there is no historical data available for analysis and no scrutiny on how it behaves on a daily basis. The author of the announcement acknowledge that its robustness is only a "likely robustness" and not a proven one.

The committee will propose "transition plans"; this is an important part of creating an alternative benchmark. Some LIBOR rate derivatives have maturity of 30Y or longer. The transition should be over that period. Any attempt to shorten that period will create risk management and valuation challenges for existing users. Solving them will require bilateral agreement specific to each existing contract; a committee imposed approach would certainly meet legal challenges.

The description of the new indices to be created can be found on the NY fed page

The exact definition of the benchmarks has not been finalized yet and the indices themselves have never been published. The proposed benchmarks are only Overnight rate; as such they are not a replacement for term LIBOR. Would the derivative market move to an overnight reference rate only market? Somehow I doubt this would be very practical for end users. Would corporate want to have daily fixing for their loans? What about floating rate mortgages?

The committee plan to publish its final report later this year. To my opinion, it will certainly take a fair amount of time, to be measured in years, before this alternative market is stabilized. If I take as reference the posts on this blog, the first one on the change of benchmark was published in 2014: Change of benchmark overnight index is a difficult task.  Almost three years later, the discussion has progress but very little has been happening in the actual derivative market regarding the benchmark.



Running Wall Street

The Wall Street Journal (WSJ) ran a piece this week-end titled "The Quants Run Wall Street Now". Some pictures of me are in the WSJ library; they took them at a presentation I gave at The Thalesians last month. They used one of those pictures to illustrate "the quants".

The picture illustrating the article is
Figure 1: Me with the first step of AAD printed on my face and the recursive formula on my shirt.

Following the article, I feel the need to clarify a couple of "details". First of all, I'm not running anything or anybody at Wall Street. You may thing that this is a pity for human society, but personally, I feel very good about it and I don't want to run anything or anybody; nevertheless I don't mind speaking to people who want to listen to me willingly. This is the case for practitioners, regulators, academics, and journalists.

Now about the content of the article. It discusses the increasing importance of "quants" in finance. It is important to clarify that a "quant" can be many things in finance; this is not done in the article and leads to confusion, like illustrating the article with a picture of me. There are several types of quants: big data quants, high frequency quants, derivative quants, risk quants, balance sheet quants (and many others, but I stop there).

The article is more about big-data quants and a little bit about high frequency quants. So the illustration of the article by a derivative - in all sense of derivative, given the algorithm depicted in the picture - quant - me -, may not be the most appropriate. On the other side, I have to confess that using a title containing "Algorithmic Differentiation" in a seminar on derivatives and balance sheet, may have confuse people looking for algorithmic trading.

I described myself above as a derivative quant. I have to add that this has been the case and is still partially the case, but I have slowly transformed into a balance-sheet quant. I'm planning to write more about that in a forthcoming blog - which I have started to write some weeks ago. Derivative pricing is about replication; replication is creating a small balance sheet composed of the option, some cash and some underlying and creating a strategy for it to maturity. The balance-sheet of a bank is simply a grown-up contingent claim. In that sense, evolution from derivative quant to balance-sheet quant is a natural evolution when growing-up.

To my subjective point of view today, I would say "The balance-sheet quants will run Wall Street Tomorrow!" Maybe that will be an article in The Wall Street Journal in a couple of years, and then the picture will be correct.

The slide that you see on the WSJ picture will be Table 2.3 in my forthcoming book Algorithmic Differentiation in Finance Explained. The very last corrections of the proofs are with the editor as I write. I'm still hoping for an availability in libraries before the summer holidays.

Thanks to the WSJ for running such an advertisement campaign for my book.


Book's proofs

I have just received the first proofs of my forthcoming book "Algorithmic Differentiation in Finance Explained". After a couple of months of editorial lethargy, the matter is moving again.

Hopefully the book will be available before the summer holidays.

The book is already announced on Amazon!


Profit explain explained

I was once asked to explain the P/L explain report. Something must be wrong in my story telling if I have to explain the explanation. After the failure of my story telling career, I decided to move to story writing. This note is an attempt at starting my new career.

The full text is available as PDF:

Profit explain explained


The Thalesians seminar

I will be speaking at The Thalesians seminar on

SIMM and SA FRTB: double AD

Seminar starts at 6:30pm on Wednesday 19 April 2017 at

City University Club

Champagne will be served before the seminar, around 6:00pm.

Register at Meetup:


Algorithmic Differentiation (AD) has been used in engineering and computer science for a long time. The term Algorithmic Differentiation can be explained as ``the art of calculating the differentiation of functions with a computer.
Over the last 5 years, AD has made its road to quantitative finance. The most straight forward use of AD is to compute the sensitivity of PV to market inputs. In the frame of SIMM and SA FRTB computation, those sensitivities are the main input and having an efficient way to produce them is important.
Once the IM/Capital number is computed, there are a lot of potential analysis which are handy, like marginal IM and IM attribution. Those analysis also require some form of differentiation, this time with respect to the positions.


SIMM and sensitivity based FRTB: double AD
  • Algorithmic Differentiation and computation of sensitivities
  • First AD: fast inputs for SIMM/FRTB
  • Second AD: sensitivity of the IM/Capital itself w.r.t. sensitivities
  • Second AD applications: attribution and marginal IM/Capital


Change of benchmark overnight index is a difficult task: interview

An interesting follow-up article in Risk magazine about Swiss rate reform: Swiss rate reform in race against the clock (subscription required). With respect to the previous Risk article on the same subject, it presents a more balanced view and not only the point of view of the WG on benchmark reform. At lot of the opinions expressed are closer to what could be found in my first blog on the subject.

Chris Davis, the author of the Risk article, found my blog on the subject and contacted me. We had a roughly 30 minutes discussion. He used a lot of the background information from the discussion and from my blog for the article, even if only two sentences from the discussion were quoted.

I was surprised that my blog was not explicitly cited in the references, as would be customary when the blog presented original research and analysis and was used for background information. On my side I will continue to reference Risk explicitly when I read something of interest in it.

On top of the subjects I introduced in my previous blogs, one element that I did not forecast was presented. This is that the current TOIS market already prices the change from TOIS to SARON. In some sense, this means that the TOIS market is not the TOIS market anymore; it is a blending of TOIS and expectation of conversion to SARON.

This is a quite interesting point of view from a pricing perspective. The actual market includes the "legal jump risk" from one index to the other without compensation. The pricing of the benchmark change is now impossible, the market has already been distorted by evoking the possibility of the change to a new benchmark without compensation. That creates more uncertainty for potential disputes. In some sense, the risk is becoming impossible to hedge. If you want to price or hedge pure TOIS, there is no market for it. The fact that there is a legal jump risk in the actual instrument probably make the market incomplete. Certainly it can not be treated with a diffusion process; you have to include a one-off jump.


Change of benchmark overnight index is a difficult task: follow-up

In my previous blog, I discussed the attempt by the National Working Group on CHF Reference Interest Rates to modify the CHF overnight benchmark index. Since my blog has been published, the minutes of the WG meeting have been published on the Swiss National Bank (SNB) website. The minutes also include the list of participants to the group.

In one of the documents, an ISDA representative indicates that the guidance are "non-legally binding" and "could be used as a tool for bilaterally negotiating amendments to contracts". The core of the issue is in the "non-legally binding" and "bilateral" words, but they seem to be largely ignored in the guidance.

The issues related to the change of benchmark overnight index are of three types.
  1. Contract modification. There will be changes in a lot of contracts (OIS and CSA). That will require a bilateral agreement on each of them individually.
  2. Valuation. Changing the contracts has valuation impacts. The compensation of those impacts will need to be negotiated individually.
  3. Risk management. This should probably be the first items and has maybe not entered in the discussion yet. The original objective of derivatives contracts like swaps is risk management. For example it may be used to swap some specific risk profile into an overnight unsecured funding profile. There is no way this risk management objective can be maintained if no unsecured overnight index is maintained. It would be reasonable for end used to ask not only for the monetary compensation of the change of value of the derivative but also for the lost risk management service. A compensation for forcing the end user to bear the cost of risk between secured and unsecured funding would appear reasonable to me. Beyond legal agreement and valuation impacts, there is a fundamental risk management reason for the original framework. Is the new framework covering those risk management requirements? This is an open question.
Coming back to the minutes of the meeting, they contain, to my opinion, the same misunderstanding that were analysed my previous blog.

1. Termination or change of reference for existing trades. This requires the agreement of all parties, contract by contract. Given the current burden on legal and client relation resources in most banks and derivative users in relation to the changes in the regulatory landscape of the derivative market, I would be surprised if there are many resources available to start those discussions in the next months.

2. Rational for a compensation payment of zero. The rational presented in the document is inconsistent with the well documented and precise collateral discounting approach (see Chapter 8 in my multi-curve book) used by most market participants. The reference to a "risk-free rate" indicates a misunderstanding around clean collateral discounting.

The argument in the minutes that "as the SARON swap market does not exists, the determination of any non-zero compensation payment is nearly impossible", proves that the market is not ready for the change, not that no compensation is due.

The argument that compensation has not been applied in "similar situations" like "the change from single-curve valuation to muti-curve valuation", indicates that the situation is misunderstood - the situations are clearly not similar - and not that a precedent exists.

3. Internal risk approval. In the minutes, an appendix gives some argument for participants to obtain internal risk approval to start trading SARON swaps.

The first point of the proposal suggest to "start trading short maturities". It is fine for me to start prudently. But as a consequence, it means that generalized SARON discounting is impossible. To be able to have pricing of SARON cash collateralized derivatives based on market prices, you need a SARON OIS market up to the maturity of the longest traded derivative (not the longest SARON OIS). This part of the proposal invites to introduce the SARON OIS slowly, over a multi-year periods, and is incompatible with a big-bang in a short 10 months period.

The second point refers to VaR. It says that "Historical Volatility (HV) of the SARON fixing is below the HV of the TOIS fixing, which allows using the TOIS risk framework without understanding volatility". The first part of the sentence may be correct, but it applies to an index which is under review, in a very specific period of stress on the market due to central bank interventions. Moreover it applies to the index itself, not to the OIS rates associated to the index which do not exist yet. The OIS rates as risk factors is what would be important for HVaR. But what seems particularly surprising is the sentence second part. If all the OIS positions were stand alone, a lower volatility would (in a weak sense) lead to lower VaR. In a portfolio setting, a lower volatility of one component will lead to a different volatility of the portfolio; if the volatility of the portfolio is lower or higher will depend on the positions and the correlations between the risk factors. New positions on a new risk factor, the SARON OIS, will appear; at the start there will be natural basis positions. Does the working group suggest that a 0 VaR is a good proxy for the basis TOIS/SARON risk in a HVaR framework?

4. Regulation for margin on non-cleared derivatives. The new regulation impact on amending trades is not mentioned at all in the minutes. I refer you to item 8. in my previous blog. Don't underestimate this issue.

I have already written a blog scheduled to be published on the 1st January 2018. The blog is written as a couple of questions. Will the situations be closer to the one I predicted in the previous and this blog or closer to the expectation of the WG? To be continued!

Don't hesitate to let me know if any bookie is offering odds on the timing of the CHF overnight benchmark; I would probably put a fiver on one side. On which side? I let you guess!

My side for the bet is maybe more difficult to guess than you think at first sight. You know my opinion, but you don't know my current position on the bet and as a trader I'm more a market maker than a punter. I trade with my brain (and my own wallet), not my heart.