Marc Henrard - Multi-curve framework

I have been reading book “Rigged: The Incredible True Story of the Whistleblowers Jailed after Exposing the Rotten Heart of the Financial” (Andy Verity, Flint, June 2023) for some time. It was published several month ago, but I just finished it. To my defence, I have to say that I don’t feel comfortable reading fiction where the “bad guys” are systematically winning by cheating. The book is the story of the miscarriage of justice done in the LIBOR manipulation story. The book content did not surprise me. For anybody having worked on a (swap) trading desk, it is clear that what was described by the accusation was impossible. It is not possible for some middle level trader to create a multi-year, multi-desk, multi-bank international conspiracy over open lines, broker lines, on open offices etc. without all around them, including compliance and senior management to be fully aware of what is going on. Moreover the regulators cannot be ignorant of the situation, except pleading complete in...

The most boring, but the most read, document I ever wrote was the Interest Rate Instruments and Market Conventions Guide . The document is more than 10 years old and requires a serious update. One thing that does not require an update is the convention for money market deposit in EUR. The convention is as always ACT/360 simple interest. The official ECB rates are at 4.00%, which means that if you invest today for one year a notional of 100,000 EUR, you get an interest from 15 November 2023 (T+2) to 15 November 2024 equal to 4,066.67 EUR (2024 is a leap year). If a bank wants to trick a retail customer, he can claim that you can get an interest of 4.0556% without telling you that he is using an ACT/365F convention. The amount is the same (up to the rounding) but it sounds a lot better. You will naturally tell me that this is too much of a misleading trick and that consumer protection agencies will see that immediately and remind the bank about transparency and fair advertisement. A di...

La question de l'indexation des salaires en Belgique provoque bien des débats. Certains soutenant qu'elle nuit à la compétitivité belge et d'autres qu'elle est partie intégrante de paysage belge et que sa disparition causerait plus de troubles que de bénéfices. La première remarque à faire est que la spécificité belge n'est pas l'indexation des salaires proprement dite mais son indexation automatique et réglementée. Partout les salaires augmentent plus ou moins avec l'inflation, les grandes questions sont: " Quand? " et " Comment? " Pour le " Quand? ", les salaires sont-ils augmentés avant – une protection –, avec – une indexation automatique – ou après – un rattrapage – l'inflation. Pour la Belgique, la réponse aujourd'hui est simple et nous était déjà donnée par le grand Jacques: "avec". Pour le reste du monde (qui n'utilise pas l'indexation automatique), la réponse est plus vague et est: "Cela...

“ So much or so much sigma, that is a mathematical impossibility. ” I have seen this sentence many times on LinkedIn or similar places. The supposed meaning of this sentence is that the probability of an event corresponding to x — with x being 3 or 6 or similar — standard deviations has a probability so small that it can be consider for all practical matter as impossible. These comments are based on a misunderstanding of what “ sigma ” represents together with a confusion between “normal distribution” and “any distribution”. I write this post with a discrete distribution notation but it can be extended easily — with a little bit of extra notations — to continuous distribution. Suppose that my distribution has n points with values a i and probabilities p i = 1/n ( i = 1, … , n ). The mean is m = sum i=1 n a i p i = 1/n sum i=1 n a i To simplify further my notations, I suppose that the mean is 0. The standard deviation is the square root of variance, with variance V = 1...

I was told recently that I was a " conspiracy theorist ". I was surprised, as this was delivered as an accusation while I took those words as a compliment and agree with them. Theorist : To define this term I need the comfort of a superior authority in definition: the Oxford dictionary.  Theorist : "A person concerned with the theoretical aspects of a subject"  Theory : "A set of principles on which the practice of an activity is based. I would certainly not deny that I'm a theorist, I embrace it. I do theories as a permanent activity: how to price a FRA? How to transition benchmarks? How to hit a draw? How to hole puts? (Those two last items, with limited success) When to buy biscuits? As a mathematician, an (honorary) academic, quant, how can any one think that I'm not a theorist or I would deny it? I cannot imagine a theory that would explain such thinking! Also I'm principled based (not rules based) and a practitioner, so a set of principle...

Constant Maturity Swaps (CMS), nom d'apparence barbare et qui semblait réservé aux temps des excès d'avant la crise financière ... mais que certains au parlement voudraient imposer à tous les petits épargnants et aux banques. Pour m'expliquer, je fais d'abord un petit détour de plus de 10 ans en arrière, au temps de la "commission Dexia". Le détour semble un peu audacieux, mais ces deux évènements sont liés, par l'incompétence financière de certains. J'ai toujours des textes que j'avais écrits alors et qui me servent d’inspiration pour ce post. En 2011, Dexia S.A. a fait faillite, pas légalement faillite, mais c'est parce que nous, les contribuables Belges y avons injecté quelques milliards. Cette entité, distincte de Belfius (anciennement Dexia banque Belgique), continue à exister et à perdre de l'argent. Cette entité étant historiquement liée à l'état Belge, le parlement a créé une commission Dexia. Les conclusions de cette commissi...

For more than a decade, collateral discounting as been the de facto standard for derivative valuation. The central technical concept of this approach is the expectation under a currency — but not collateral mechanism — dependent measure. That measure is denoted in part of the literature. This is the notation I used in my Multi-Curve Framework with Collateral paper in 2023. This is the paper that developed the details of the “collateral square” valuation, when the collateral is is an asset that can itself be used into a repo to obtain cash. The generic formula in that latter case is (originally described in formula 13 in the above paper). The measure X appears in the expectation and is central to the approach, based on replication. It mathematics, it is traditional to add some marker (like a tilde or a bar) on some symbols to indicate another object similar or generated from the first one. One symbol that I like is the "check", which I called when I was lecturing in fren...

IOSCO has issued a document called “Principles for Financial Benchmarks” in 2013. As such it acted as an (unofficial/unelected) lawmaker. On 3 July 2023, the same IOSCO issued a “ Statement on Alternatives to USD Libor ”. The Statement looks like a tribunal judgement from a trial with no public hearing, no witness, and no defense right from a tribunal with no mandate to judge. And publish on the day before Independence Day! Some personal comments on the document. Transparency The statement indicated “Administrators should consider whether to improve the transparency of their rates". The IOSCO document lack minimum transparency. It does not indicate in any way the “varying degrees of vulnerability of concern“ of the analysed benchmarks. The name of the benchmark are not even indicated. This creates a culpability by association to all non-SOFR benchmarks. The statement refers to a Review of Alternatives to USD Libor ; to my knowledge, the review itself is not available. The st...

If you read this, it means that the world has not ended! Good to know the world can exist without LIBOR. Actually some GBP-LIBOR fixing will still be published to the end of March 2024 and some USD-LIBOR will still be published to the end of September 2024 due to FCA use of “Article 23A benchmarks”. Maybe I penciled the wrong “end of the world date” in my calendar! New “real” LIBOR (by opposition to the one invented by FCA) fixings are not published anymore, but old fixings still exists. We can see almost 10 trillions of it in the LCH data of Outstanding IRS. In number for 30 June 2023 on USD 3-month tenor: LIBOR fixing 5.54543 CME SOFR Term Rate: 5.26936 ISDA Spread: 0.26161 “Synthetic” LIBOR: 5.54543 There is a 1.546 bps gap somewhere! Where would that be? According to market rumours, both LIBOR and CME SOFR Term Rate are representative market rate as of 30 June 2023. We can only conclude that ISDA Spread is not a representative market rate. Why it will be used fro...

L’inflation des prix de l’alimentation fait des ravages. Maintenant 1,09 EUR est moins de 1,00 EUR. A ce prix là plus moyen de nourrir les cerveaux. Faut-il envoyer le responsable en prison pour publicité mensongère ou à l’école primaire pour une petite révision?