Marc Henrard - Multi-curve framework

IBOR transitions (mainly LIBOR transition for the moment) is a huge undertaking for the derivative markets. It implicates many market participants, from large dealer/broker to small end users. Everybody want the transition to be perceived as " fair ". Reading trough the regulator published notes, FAQ and letters, I notice that I don't have the same definition of " fair " than some regulators. This leads to my question in the title: How low is the regulators' bar? To illustrate my point, I will take two examples, one from the FCA and one from the CFTC . The italic texts below are extracts from the regulators and ISDA documents, the regular text are my comments. FCA The FCA published a " Questions and answers for firms about conduct risk during LIBOR transition ". Treating customers fairly when replacing LIBOR LIBOR discontinuation should not be used to move customers with continuing contracts to replacement rates that are

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 year ago, I was reporting A two cent arbitrage - free options . When the minister in charge (the minister was then Kris Peters , now member of the European Parliament - Kris Peters ) of "financial products" and financial regulators ( FSMA ) is not a quant, you know you are heading for financial troubles. To make a long story short, since 1 December 2019, in Belgium for each retail transaction, you have a free option. If you pay in cash, the total price is rounded to the nearest 5 cents, if you pay by card, the total price is not rounded (it is a little bit more complex than that but for the sake of a short story, this is good enough). The arbitrage strategy is easy. If the total price of the purchases is ending by 1, 2, 6 or 7 cents, pay by cash and get a 1 or 2 cents discount. If the total price ends by 3, 4, 7 or 9 cents, pay by card and pay the exact price. In case of 0 or 5, do whatever is most convenient. With this strategy, on average (if the last figure of

Winter weather in Belgium, but good winter weather! Dry and warm enough for a reinvigorating 18 holes golf. And on top of the good air cake, my best score ever. Started on the hole 1 with an eagle and finished 17 holes later with a gross score of par +1. Enjoying my winter!

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

BMR update has been published on 27 November 2019; its main effect that were to take effect one month later have been delayed by 2 years. The full text is available on EUR-lex: https://eur-lex.europa.eu/eli/reg/2019/2089/oj The natural question here is: Marc, have you been asleep since 27 November that you did not notice this very important piece of legislation being published? The answer is: Yes, I have been asleep part of the time, usually at night. Actually I had read the title of that piece of legislation but I deemed it to be of no importance for interest rate benchmark transition. As a (weak) defense to my failure to see the significance of this piece of legislation, I will only present the title of the document published on the Official Journal of the European Union: REGULATION [...] amending Regulation (EU) 2016/1011 as regards EU Climate Transition Benchmarks, EU Paris-aligned Benchmarks and sustainability-related disclosures for benchmarks . Yes you read that correctly. A

This morning I was reading the article in Risk.Net titled Compounded rate out of favour, finds Japan survey published yesterday. My reaction was: I have heard that before, what now? Let me explain this with a little bit more details. For this I need to quote a couple of sentences from the article that are part of the "I have heard that before": A majority of market participants in Japan want to use forward-looking term rates instead of compounded risk-free rates as a reference for new loans and floating rate notes. Similar findings had been obtain for EUR fallback (including derivatives) when the forward-looking term rates were included in the option list. The article then indicates: The preference for forward-looking rates, two dealers say, is due to a lack of familiarity with Japan’s designated risk-free rate, Tonar, coupled with an ignorance of the challenges in developing a robust forward-looking benchmark. This is taking the problem the wrong way. The quest

The Federal Reserve Bank of New York has requested comments on its Proposed Publication of SOFR Averages and a SOFR Index . The proposal and the request for comments is available on their website at https://www.newyorkfed.org/markets/opolicy/operating_policy_191104 . My comments are reproduced below. SOFR Averages In general, I consider that the publication of official numbers related to payments to be made by end users in financial markets is to be encouraged. In the context of the transition of some financial products to more usage of overnight rates, proposing a ready made composition / average would be beneficial in certain circumstances. Unfortunately the proposed 30, 90, 180-day periods do not correspond to any existing or planned financial product (except in unlikely cases when 1, 3 or 6 month exactly cover that round number of days). The introduction of averages published by an official institution but that do not cover exactly and in all circumstances the requirements of t

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!

At the end of November 2018, I took a GBP (paper) position on my view that LIBOR fallback approach will allow better informed participants to make money (transfer value from) the end-users. I have reported on a regular basis about that position in the first six months (see list of episode at the post bottom). One year later, what happen to that view and to my position? I'm happy to report that Saint Nicolas brought me a very nice present ( Saint Nicolas is an important day in Belgium for good kids like me ;)). On 29 November 2018, I wrote The horizon for my position is 29-Nov-2019. Target profit is 5bps x ~2000 GBP/bps = ~10,000 GBP. I cut the position on the earliest of when the market has reached 8.5 bps or on 29-Nov-2019. I'm also expecting a little bit of carry as the current level of realised spread (1 to 3 bps) is below the market basis spread. Where do I stand today? According to my figures, in term of spread convergence, the spread has decrease by 4.5 basis poi

According to the recent ISDA consultation, the fallback spread above RFR will be based on median historical spread over a lookback period of 5 years. One issue that I did not raised in my answer to the consultation is the definition of median (it was so obvious to me that a median would not be selected, that I did not bother; I know, I was wrong again). The median of a random variable is (see for example the Wikipedia definition ) is any real number m that satisfies the inequalities P( X ≤ m ) ≥ 0.5 and P( X ≥ m ) ≤ 0.5. The tricky part is in the " any " for discrete distribution (like an historical distribution). If there is an even number of days in the 5-year lookback period (the exact meaning of 5-years is still unclear), there are infinitely many of such numbers. With the 7 decimals on LIBOR (5 decimals when expressed in percent) and the composition on many days on irregular period for the overnight part, it is very unlikely that the two numbers in the mid

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

An important quant software provider proposes a webinar titled: Impact Analysis: The 2020 Clearing House Switch from OIS to SOFR Discounting It seems they don't understand what OIS is and what OIS discounting means. Please read my multi-curve book , Chapter 8 for the details. A meaningful title would be The 2020 Change in collateral rate at CCPs from EFFR to SOFR: discounting transition

alea iacta est (actually almost " est ") The results of " The Final Parameters Consultation " have been published . The winner is " historical median approach over a five-year lookback period " with " two banking day backward shift adjustment period ". The exact meaning of this has been subcontracted to Bloomberg. This clarifies that the " final " adjective in the consultation name was related to the consultation, not to the parameters . Clearly ISDA did not listen to my suggestion of publishing the results when markets are closed and announcing the publication date in advance. My suggestion was made in order to limit the impact of non-public material information. But I guess that those issues are not deemed important in this circumstance. Probably the lawyers don't understand the impact of information on derivative valuation. Let me remind you that present value in s is N s E[(N t ) -1 Pay-off t | F s ] It dependents

I just finished reading Fahrenheit 451 . Certainly not a new book but a new reading for me. A world where books are outlawed and burned to the last one. The burning is not due to the physical books made of paper, but due to their content. Books contain truth, history, and imagination. All of them dangerous to status quo seeking classes. Luckily this is a world of fiction and the books are not (yet) forbidden. A world of fiction, as should be a world where some people a jailed and tortured for publishing the truth, a world where some people are jailed and tortured for expressing opinions. Unfortunately, in our world those issues are a reality, including very close from home.

Another episode in the finance fiction series! Everything below is pure fiction. I'm an end-user with a LIBOR swap transacted with my trusted bank on a bilateral uncleared basis. I receive LIBOR (and pay fix) for 10 years. I don't sign the ISDA proposed fallback protocol and my swap stay under current ISDA definitions. Move forward to the future: Come the first reset date after the discontinuation date. The LIBOR rate is not published on Reuters screen LIBOR01. We call four reference banks in London at 11:00 am London time, none of them provide a quotation of its rate. We call four reference banks in New York at 11:00 am New York City time, none of them provide a quotation of its rate. The fallback in the ISDA definition stops there (See ISDA definitions, Article 7, Section 7.1. Rate Options. (ab) U.S. Dollar. Paragraphs (xxii) and (xxv)). We can not agree on a rate on a bilateral basis with the bank counterparty. We go to court/arbitrage to get an independent assess

I finally found the answers to the second ISDA consultation on IBOR fallback. It has been published on 19 September, but somehow you have to navigate through a layer of webpages to find it. It never appeared on the ISDA news. To my knowledge, the only link is on the last line of the announce of the consultation on final parameters. The direct link is https://www.isda.org/a/0LPTE/2019.09.18-Anonymized-ISDA-Supplemental-Consultation-Report.pdf The report contains manipulation of the results, false claims, violate standard academic copyright fair use by not attributing to the authors in a recognizable way. Manipulation 21. If the respondents’ ranking preferences to the 2018 Consultation were such that the compounded setting in arrears rate with historical mean/median approach was not the preferred combination (i.e., ranked second or lower), these respondents also were treated as answering “Yes” to Question No. 1 of the 2019 Supplemental Consultation as long as the respondents were

I'm preparing my answer to the `` Consultation on Final Parameters for the Spread and Term Adjustments in Derivatives Fallbacks for Key IBORs '' issued by ISDA. By reading the questions at the end of the consultation, I have the impression they have at last read my July 2018 and  January 2019`` quant perspective '' (available on SSRN here and here ). A lot of the questions asked in the consultation were debated there: negative " spreads " (monetary policy misestimation), proposal not achievable and requiring shifts or lockouts, holiday calendar problems, shift and lockout workaround not working, calculation period instead of IBOR period. Maybe I should start my answer with "I told you". Even if my fingers are itching, I will make an extensive effort and answer the consultation in a business-like fashion in my official answer. But in my blog, I can let my fingers fly and make blog-like answers! Q: Which cities should apply for the purposes

A first ESTR swap has finally be traded. The trade is reported in Risk.Net: ESTR swap trading gets under way   It is a EUR 100 millions, 1-week swap traded on 30 September (effective date 2 October) between HSBC and JP Morgan. I know that ESTR will be published only as of today (actually yesterday rate, because of T+1 shenanigan) and people will argue that it was not possible to trade before and my "finally" is not warranted. I strongly disagree with that, as explained for a couple of months in some blogs ( here and here ). One could have traded forward start swaps or swaps with a pre-launch fallback to EONIA - 8.5 bps. Moreover, CCP will accept clearing only on 21 October 2019 for LCH and 18 November 2019 for EUREX. CCPs explain their delay in providing that elementary service by the requirement for "client to be ready" (see my take here ). There was no logical requirement for client to be ready for the CCP launch as clients are not obliged to clear those tr

The Federal Reserve has manipulated SOFR again. This time not by replacing the actual trade data by a survey of dealers but by directly trading will dealers at off-market prices. The bail-out trades (overnight repo operation) have resulted, as intended, in lower reported SOFR rates. It is true that the rates were originally distorted higher due to government intervention, and the Federal Reserve, an other government body is intervening to distorted the rates lower. The results of all those interventions and distortions is that we don't know where the market really is. And the regulators are pushing for this heavily distorted number to be the base of the interest rate market. What could go wrong with such a system? As I'm at it, the CCPs are pretending that they can summarised all those distorsions into a big bang change from EFFR to SOFR for collateral PAI and discounting using a simplistic valuation mechanism for compensation. And ISDA is asking how to compute the sprea

CCPs have announced their plans regarding ESTR swap clearing. Some plans are described in a Risk.Net article titled " LCH sets €STR swap clearing launch date " (subscription required). Some of the claims there exhort me to react: 1. On the valuation and margining side, the fixed 8.5 basis point spread between Eonia and €STR means that we think it’s possible to use Eonia as a proxy for €STR as a risk factor. Whitehurst says. For the valuation, I agree: in October, EONIA will be equal to ESTR+8.5bps, so you can convert from one to the other. For the margin side (initial margin), it seems that they use logic in the wrong direction. You can use ESTR history (that does not exists yet) to predict the future of EONIA (that will soon stop to exists but in the mean time is related to ESTR). You cannot use the EONIA history (that was not linked to ESTR) to predict the future of ESTR (that will start to exists in October). I don't say that it is

One of my recent papers related to the LIBOR fallback has been accepted for publication in Wilmott Magazine LIBOR: Don't fallback, step forward The paper will be published in the November 2019 issue. I will present the main results at a CQF Institute seminar on 18 September 2019 . Abstract There is a general consensus that LIBOR's publication will be discontinued in the coming years. The best preparation for the discontinuation is to transition all trades, new and legacy, to different benchmarks. The option of last resort is to rely on the fallback language of existing contracts. The language for derivatives is currently not fit for purpose and is in the process to be reworded. In recent months several fallback-related consultations have taken place. The theme of this article is the fallback proposals. To the author point of view, the proposals are not satisfactory; the main proposal is not achievable in practice and a fundamental revision of the fallback's foundati

One of my recent paper related to the LIBOR fallback has been published in the risks journal: LIBOR Fallback and Quantitative Finance The full text of the article is available as Open Access article on the journal website.

On 5 June, I published a post titled The Fed Manipulated SOFR . On 6 June, Risk.Net published an article titled A mystery: Why did the NY Fed use a survey to get SOFR? (subscription required). The Fed corporate communications has published a comment in Risk.Net that is supposed to be a rebuttal of those analysis . I was expecting rebuttal to be an argument on the quality of the market infrastructure put in place but I only heard " you cannot sue us for this issue ". It is true that the information on the production of SOFR is available in the Fed Website . But when the Risk.Net article was published, " A spokesperson for the New York Fed declined to comment. ", proof that it was not obvious even for the Fed; the "comment" referred above was published only on 18 July (more than one month and an half after the data); the CRO of a large bank when asked at an industry conferences said that he had no idea what happened. All those small items are evidences

One of my original papers on the multi-curve framework has now attracted more than 4,000 downloads on SSRN. The first paper was published in July 2007, before the start of the crisis and was titled The Irony in the Derivatives Discounting . The second one, posted shortly after the crisis, was naturally called The Irony in the Derivatives Discounting Part II: The Crisis . My papers posted on preprint servers (RePEc and SSRN) have now attracted more that 50,000 downloads (and my multi-curve blog that you are reading now, more than 86,000 visits). Thanks for reading my Irony !

My answer to the May 2019 ISDA consultation titled " Supplemental Consultation on Spread and Term Adjustments for Fallbacks in Derivatives Referencing USD LIBOR, CDOR and HIBOR and Certain Aspects of Fallbacks for Derivatives Referencing SOR " is now available. The document has been posted on SSRN with abstract ID 3415930 . It has not been "reviewed" yet but is already available. Comments are welcome! This answer is a follow-up on my answer to the July 2018 consultation on similar subjects .

On those first day of the summer holiday season and waiting for the 4th of July we can ask ourselves if lenders are all on holiday. As usual, the month-end print of SOFR was higher that other days of the month. The end-of-month, including a week-end, had a rate of 2.50% while Fed Funds were are 2.40%; a 10 bps difference. Nothing unusual. On the first day of the month, SOFR was 3 bps higher that Fed Funds. Nothing unusual. But the 99 percentile rate was 3.85%, 143 bps above the median. This is very unusual. 1% of the notional traded on that day, which amounts to roughly 12 billions, was above 3.85% Who borrowed those 12 billions secured paying so much? On the second day of the month, the print was 2.51%, this is 11 bps above Fed Funds and 1 bp above month-end. This is relatively unusual. The 99 percentile was at 3.10%, 59 bps above the median. This is also very unusual. What will be the print over the 4th July? Should I be ready to incorporate the 4th of July as a seasonal effect i

This could be classified as another episode of finance fiction! In this period of consultation related to the LIBOR fallback, I would like to describe an option which, to my knowledge, has not been mentioned yet: physical settlement. It is not new by itself and not a panacea for the fallback, but maybe it could have a couple of niche applications. To introduce that approach, I will take the case of caps/floors. If the fallback mechanism is based on compounding setting in arrears (1), as it is envisaged today, the cap/floor optionality changes dramatically. The current LIBOR caps are European options with expiry on the LIBOR fixing date; the post-fallback caps would become Asian options on the composition of overnight rate between the start accrual date and the end accrual date. This is a significant change in term of complexity and valuation mechanism. By luck, I wrote a formula that can price those instruments in a simple one-factor model more than 10 years ago in Henrard (2007).

Interesting article in Risk.Net on "making money on LIBOR fallback". The title of this blog is the title of the Risk article published on 19 June 2019 (subscription required).  The title between inverted comma above is the title of my series of blogs on the same subject, the first of which was published on 30 November 2018 . The Risk article was in part inspired by my blogs, as you can see from the references to the figures I computed and the link to a recent muRisQ blog on the flatness of the GBP LIBOR-3M/SONIA curve .

A couple of weeks ago, I reported a manipulation of SOFR by the Fed . I have now to report an "incident" of unknown nature. The SOFR (and Effective Fed Fund Rate) data is not accessible anymore on the Fed website. But at the same time the data is still available in Bloomberg. Does that means that the results of public service work (the Statistics computed by the Fed) are not anymore a public good but can be accessed only through private services requiring a payment to a private company? It will be interesting to hear the explanation about this problem. I have not heard any explanation for  the "feed" problem of last month end. What actually happened? What would have been the SOFR fixing if the actual data had been used (and not a survey)? Edit Monday 24-Jun-2014: The page is up and running again. To my knowledge, there was no explanation why it was down yesterday. I will now be able to update my SOFR analysis...