Marc Henrard - Multi-curve framework

Everybody is familiar with the option exercise mechanism ... expect fictional Belgian lawmakers. A (real) judge once said: "it is not illegal to be smarter than tax collectors". To be precise, what he actually said, was "It is not illegal to be smarter than your counterparties [...]" , but in tax matters, the tax collector is your counterparty. What we explore in this financial fiction blog, is to assess if it is possible to make money out of the ignorance of fictional lawmakers. This is a work of fiction. Characters, places, and events are products of the author’s imagination. Any likeness to real people, living or dead, or actual events is by chance almost everywhere.(1) This blog does not contain any financial or tax advice. The taxation of options is done in the following way: if an option is bought then sold or the opposite, the profit or loss on the buy/sell is taxable. If an option is exercised, the option price is ignored for tax purposes, but the transa...

" La Banque nationale de Belgique s'attend à une perte de 3,7 milliards en 2024 " S'attend? Nous sommes le 17 janvier 2025, l'année 2024 est finie depuis longtemps, d'où vient l'incertitude? Je sais que les prévisions sont difficiles, surtout quand elles concernent le futur. Mais ici on parle du passé. Quand j’étais trader sur un desk de taux, il y a plus de 15 ans, les profits (P/L) on les calculait chaque soir avant de quitter le desk et on vérifiait avec le rapport de middle-office le matin. La puissance de calcul a-t-elle tellement diminué depuis? Il faut plus de temps pour faire les multiplications et additions? Exactement le même titre et le même texte dans les 2 journaux belges francophone principaux – “par Belga”. Pas une analyse, pas un journaliste qui fait une remarque, pas de quatrième pouvoir! Si ce n’est ce blog insignifiant que vous êtes en train de lire? Journalism is printing what someone else does not want printed; everything else is pu...

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...

“ 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...

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...

When I created my consulting firm, I called it muRisQ (standing for management of Risk by Quantitative methods). This was before SARS-CoV-2 escaped from Wuhan. In the mean time, the WHO has changed its naming convention for variants and is using the Greek Alphabet and not the place of original detection anymore. After the original Wuhan Coronavirus, we had the Kent, South Africa and India variants; they are now called Alpha, Beta and Delta. Now there are so many variant that the letter " mu " as been reached at the end of August. Luckily for muRisQ, mu is a " Variant of Interest ". It could have been worst with mu being a " Variant of Concern ". But it could have been better if I had called the firm nuRisQ or xiRisQ. For some reasons that escape me, the WHO has skipped those two letters and has jumped to " Omicron " recently. Without risk of libel, I can now write that the WHO is an analphabet organisation: "Analphabet: Characterized by i...

LIBOR transition is involving large value transfers between market participants. In the past, I offered to my faithful readers the possibility to make money on LIBOR fallback (see the series starting here ). The money making machine required to take some "spread positions" and trust that the LIBOR cessation process would complete in a time frame of a couple of years. The LIBOR cessation completed on 5 March 2021 with the announcement regarding the forthcoming cessation. The term "position" above is in between inverted commas because the point was that it was not really a spread position from a market risk perspective, only from a name perspective. It turns out that there is a little bit of market position in the trade as described in Fallback transformers: gaps and overlaps and the following muRisQ's blogs. The position I proposed In November 2019 has made more than 10 bps in rates . Now that you have made some money with hard work, I propose a mechanism to lo...

Almost three years ago, on 30 November 2018, just after the results of the first ISDA fallback consultation were published, I explained " how to make money on LIBOR fallback ". There were many episodes to the series (see list below) but I never concluded on that first part. The conclusion came in March 2021 with the publication of the ISDA/Bloomberg fallback spreads. Those spreads have transferred huge amount of money between market participants. I hope you were on the receiving end of the value transfer. What is the order of magnitude of the money transfer? I don't know, as I don't now the positions of the different market participants. But at least I can tell you how much money you would have made if you had followed my advise from November 2018. Then I indicated that " I enter into a basis swap where I pay LIBOR-1M v receive SONIA + spread on a 30-year tenor for a notional of 1m. The current spread is at 13.45 bps. My analysis gives me a 4 to 8 basis points ...

Good to see that the Yield Futures design that I proposed almost 10 years ago is finally trading. CME has announced a “strong liquidity on launch day” for its Treasury Yield Futures . Some notes on the design I proposed are available as a blog: Risk-based futures and a working paper for the overnight-linked version: Risk-based overnight-linked futures - innovative design . Originally the design was proposed with several variants for the underlying (LIBOR swaps, OIS, bond/treasury) and delivery mechanism (cash settled or physical settled, notional based or risk based delivery). All the variants have the same mechanism as their main feature: quoted in yield and PV01/risk based daily settlement.  In some sense it was not even an original design as the fixed PV01 mechanism was already used for LIBOR futures. But the extension to other products was new and the idea of smooth risk at delivery was also new. Unfortunately the smooth risk feature has not be retained by CME. The futures a...

After some financial fictions, here is a food fiction. Following price manipulation and decrease of volume in cookies, the cookie market is going through a reform. There are always tough cookies. To deal with them, the Factory Cookie Authority (FCA) has decided to ask for more power to the parliament. The proposed power would allow the FCA to impose synthetic prices on cookie contracts. The cookie prices will be based on the flour price plus a fixed spread. The spread has been decided by the International Cookie Dealer Association (ICDA) after a public consultation answered by a less than 100 people, mostly ICDA members. The spread is a fixed number for the next 50 years and is not based on cost of other cookie ingredient, like sugar, eggs, salaries, taxes, but is based some on historical figures selected by ICDA mixing (pun intended) flour, sugar and rotten (i.e. in-arrears) eggs over different periods. Should the MPs vote for such a tough cookie power? Wouldn't that be a tough co...

French Christmas song adapted to this year: Mon beau Libor, roi des indices Que j'aime ta simplicité Quand par ISDA, contrats et accords Sont dépouillés de leurs attraits Mon beau Libor, roi des indices Tu gardes ta droiture Original text: Mon beau sapin

There are multiple discussions about bilateral IM for FX forwards and FX options, specially with category 5 coming into play next September. See for example the recent Risk article Margin rules snare FX options user (subscription required). Personally, I never understood why deliverable FX spot and FX forward were excluded from the framework, except perhaps that they had better lobbyists. I don't understand the " spirit " behind that rule. One propose workaround proposed to include some deliverable FX forwards is to use zero collar options to hedge the delta risk, in a way similar to what is done for IR swaps. There is another method that, to my knowledge, has not been publicly discussed before and which is to my taste nicer. And it does not involve options. Instead of a physically settled forward, one can trade a pair of forwards with one non-deliverable forward at the same date and rate one physically settled forward, the strike of which is set on the non-deliverable f...

Reading the Bloomberg IBOR Fallback Rate Adjustments Rule Book just published. I'm trying to understand the period for RFR composition. It looks that the period is based on the LIBOR tenor. It is not the " calculation period " that was used, but never defined, in the consultations. Do I misunderstand something or there is something strange with the " two days shift " and the " two day shift " may actually be a 0 day shift with respect to the payment date? Do we end up having to pay same day in some cases? My understanding of the dates and offsets leads to the following example, using the coming Monday as an example. I have a XXX-XIBOR-1M with effective date Friday 2020-03-27. The maturity date is Monday 2020-04-27. The "Accrual Start Date" for the composition has an offset of 2 business days and is Wednesday 2020-02-25, the "End Accrual Date" is 1 month later, i.e. Saturday 2020-04-25, adjusted to Monday 2020-04-27. I'm...

On 6 March 2020, the ARRC published a document on a proposed legislative solution for the USD LIBOR contracts . I read in the ARRC document the confirmation of the cautionary tale published published in Risk.Net a little bit that a month ago. The markets movements over the last days had already confirmed the legitimacy of such a caution. An updated version of the graph published in the tale is proposed below I'm using two extracts of the document to justify the claim of the ARRC's confimation: Alternatively, many parties would likely choose to litigate the outcome or otherwise ask the courts for direction. This is the starting point of my tale, the start of the " fiction " part of it. A fiction now corroborated by the ARRC. For ARRC also it is natural that the affected parties will ask an external arbitrator (the courts) for direction and naturally the arbitrator will base its decision on information available at the time of the decision (not only based on...

Inspired by my previous post . Belgium produced many astonishing people, the two best known of them a purely fictional characters: Tintin and Hercule Poirot. Among the non-fictional Belgian characters is Jacques Brel. The famous singer was so influential, that his song with a Latin title Rosa and a Latin chorus Rosa rosa rosam Rosae rosae rosa Rosae rosae rosas Rosarum rosis rosis has now inspired the Federal Reserve Bank of New York for the publication of SOFR averages . Qui vont à ceux qui ont la chance D'apprendre dès leur enfance Tout ce qui ne leur servira pas Jacques Brel That goes to those who are lucky enough To read the publication as early as 2 March Of all those SOFR averages they don’t need Federal Reserve Bank of New York

LCH is proposing to changes the LCH Limited Rulebook. The details can be found at: https://www.lch.com/membership/ltd-membership/ltd-member-updates/lch-limited-rule-change-committee-10-january-2020 This post is a work of fiction, an extreme fiction. The official narrative is also a work of fiction, also an extreme fiction and consequently I feel allowed to write my own fiction about this very important topic. Reality is probably between the extremes of fiction. You can't have your cake and eat it too CCPs want fees related to risk management of large portfolios but at the same time want to get rid of the risk as soon as the risk is about to materialize. Default fund and margin haircut on the materialization of credit risk through default, default fund usage in case of bad management of their funds investment process, and more recently remove LIBOR risk as soon as there is a LIBOR discontinuation risk is about to materialize. This is this last point that interests us here. F...

This is pure fiction. Any resemblance to real events, situations, or persons, past, present, or future may or may not be purely coincidental. Any resemblance to fictional characters is intentional! Pharaohs and Gods At the time, Egypt was ruled by Pharaohs. When becoming Pharaohs, the human beings were also becoming Gods. They joined the gods like Isis, Horus, Ra, and others. For some time they were both human beings and gods. When their human being bodies died, they were buried but they stayed god forever. The disturbance of the bodily remains of those gods induces well documented curses: the curse of the Pharaohs . Whoever open the God's tombs was cursed for life, usually a very short life. Libor: universal God The curse stroked back three millennia later when a new God emerged: Libor. By opposition to the Pharaohs, Libor was not born in a human body to become god. Libor was fully immaterial, a pure number; even if its representation by human started on a specific date ...

A recent blog of mine was titled " Compounded rate out of favour: what now? " In this post, I try to answer my own question by proposing some solution for the loan market. I believe it can accommodate both sides of the issue: having interest rate based on overnight compounding in arrears and at the same time fixed amounts known at the start of the period. Suppose that you had previously a one year loan with floating rate based on LIBOR-3M with payment of interest every 3 months and potential repayment of part of the notional after each of the 3 months periods. What does the bank want: overnight based market risk. What does the bank accept: loan term credit risk on the end user for the stated notional. What does the end user want: floating rate with amounts paid at the end of each 3-month period known at the beginning of the period. Those requirements may appear contradictory but they are not as described here. At the start of the first period, a temporary fixed rate i...

Summary of a recent quanty discussion about LIBOR fallback. How to price a LIBOR payment with the current fallback: Estimate the expectation of the discounted values of question marks. How to price a LIBOR payment with the planned new fallback: Estimate the expectation of the discounted values of the median of future values of question marks strongly impacted by market misestimations. No doubt, we are making good progress!

EU BMR is in forced since 2018 (with some transition period to 2020/2022). Different rate transitions are expected in the coming years: new fallback definitions, CCP discounting big bang and GBP FRN conversions. For each of those transitions I have questions about the compliance of the proposed solution with EU Benchmark Regulation. I have not received or seen clear indications, e.g. an explicit message from regulators, about the compliance. I have asked those questions in different context, including directly to the regulators in some cases, but have not receive answers. I post the question here in the hope to receive answers. I will add the answers if and when I receive them. 1) Fallback language In the proposed ISDA new definition, a spread based on the historical data computed on the announcement date using 5 year median is used. Are the full 5 years of historical data EU BMR compliant? LIBOR is compliant since 2018, SOFR has been published since April 2018, SONIA has been refo...