Marc Henrard - Multi-curve framework

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

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!

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...

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 purel...

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

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 . ...

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 Professor RWTH Aachen University

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. Rant on books!

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 dV t and payment linked to a benchmark c t V t ...

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.   The future of LIBOR (FCA, 2017-07-27) No Room for Error: A Misstep in Creating an Alternative to Libor Could Be Costly to Investors (PIMCO, 2017-08) Looking Past Libor: What’s Next for Investors? (PIMCO, 2017-07-27) Bidding A Farewell To LIBOR (Seeking Alpha, 2017-07-30) LIBOR Replacement Plans Bring Regulatory Considerations for Derivatives (Skadden, 2017-08-15) Don't hesitate to add more references in the comments.

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 Un-manipulable 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. Observable 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...

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 ...

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.

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 ...

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...

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

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

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 art...

[...] 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

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 severa...

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 alterna...

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"...

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 !

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

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: https://www.meetup.com/thalesians/events/238981871/ Abstract 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 anal...

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 sub...

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. 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. Valuation. Changing the contracts has valuation impact...