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)