Imformation Age since ... 20 years

Last week-end I visited the Science Museum in London, and more precisely the Information Age new exhibition. One of the displays describes the invention of the “WWW” at the CERN in the early 90s. One of the dates that attracted my attention in the panel was the date of the first WWW conference: May 1994. The conference's site is still working!

This reminded me that I was an early web “designer” (you can decide what the inverted commas mean for yourself once you have seen the result). I was surprised to see that some of my early “pieces of art” are still alive, for example: http://www.ulb.ac.be/assoc/bms/bbms.html

An almost empty and obsolete since 10 years page, but still a piece of www archeology. I don’t remember when I designed the Belgian Mathematical Society first web site, but it was obviously before the 16 February 1996. That was almost 20 years ago and less than 2 years into the www history.

What I remember from the design is that the it was done by manually typing the HTML code in a text editor, selecting the colors by changing the color code in the HTML code and looking at the results.

This is not directly related to the “Multi-curve framework” book... Except in the sense that WWW was disruptive technology invented in a academic framework that has been adopted in a couple of years and became the industry standard. This is not very different to the multi-curve framework which was a academic curiosity in July 2007 and a industry standard a couple of years later, ... less the impact on the daily life of people.


Change of benchmark overnight index is a difficult task

In the book, I indicated why I dislike the term “OIS discounting” (OIS = Overnight Indexed Swap) as it hides the complexity of the valuation process and the numerous hypothesis and results required to achieve the valuation formula. The correctness of the approach depends on a number of market conventions and practice, unstable to my opinion. Unstable in the physical sense, that a small perturbation to the situation can destroy the whole process, not only move it slightly.

This blog entry is written in reaction of the Risk article titled OIS rate change easy to absorb, says ISDAs O'Connor (subscription required). As you can guess from the introduction, I disagree with the “easy” part of the title and I believe the term “OIS” used in the title is as misleading as the one used in “OIS discounting”.

If I understand correctly the article, there is a General Collateral (GC) overnight index and some suggestion, in particular by the US Federal Reserve, to change the standard index from Federal Fund
Effective rate to the GC index as a reference for the OIS swaps, as a rate paid on cash collateral under bilateral Credit Support Annex (CSA) agreements and as a rate for Price Alignment Interest (PAI) by central counterparties (CCPs). The ISDA’s chairman seems to think that this is an “relatively easy” change.

The index used would be the GC index published by DTCC: http://www.dtcc.com/charts/dtcc-gcf-repo-index.aspx

Let’s start by a positive comment. The cash collateral referred to in CSA applies, by definition, to a collateralized situation. The derivatives are collateralized by the cash and the cash is collateralized by the derivatives. It seems appropriate to use a collateral rate to remunerate the cash; the GC index is an appropriate index.

The idea of using another index is not a bad one in a stable situation. But the proposal does not only concern a stable situation, it is supposed to apply to a change to the new index. A change is a very different proposal. The “OIS discounting” by clearing houses and for bilateral contracts works only because
  1. The rate paid on the cash collateral (and the PAI) is linked to the same overnight index for its entire life.
  2. The rate reference in the OIS is the same index.
  3. The OIS themselves are collateralized with the same rule as the other instruments for the entire life of the OIS.
Suppose we decide to change the rate paid in PAI in central clearing to the GC index. To create the stable situation that allows a clean and standard valuation, the following steps are required.
  1. Create a liquid OIS market linked to GC.
  2. Make sure that bilateral traded new OIS refers to a (new) CSA related to GC collateral interest
  3. All dealer have to sign new CSA agreements for the new trades
  4. CCPs create a new category of trades with GC collateral; it is not possible to net the existing trades and variation margin as the trades have different reference collateral rates and no full netting is possible. Cross margin for Initial Margin (IM) is probably possible, but not at the Variation Margin (VM) level. Or more exactly a payment netting is possible but not a netting of new and old instruments in term of positions.
  5. Run, up to the maturity of the longest trade existing in the world linked to fed funds, two parallel markets, one for the Fed Fund trades and one for the GC related trades. This includes computing convexity adjustment between the different trades (good for me, more work for quants, see Theorem 8.11). The dual collateral rules require each user to run a double set of multi-curve framework with collateral, one with each collateral.
  6. As an alternative to 4/5, users with existing position could decide to cancel the existing trades. That would require each individual user to agree on the valuation of each position and agree to cancel it for that price. The cancellation could be replaced by an alternative move from one collateral to the other, but in the same way all the parties have to agree on the valuation (as an up-front fee or a fee over the life of the trade) impact of the transfer.
Changing the overnight benchmark index has a greater impact that changing the LIBOR benchmark index. The overnight index is used as reference for OIS but also, and this is the trickiest part, as a reference index for standard CSA collateral and CCPs. Not only all the trades that refer directly to the index are impacted, but also all the trades that refers to it indirectly, through collateral rate or PAI. This is roughly all the OTC interbank market.

My conclusion: OIS rate change very difficult to absorb (due to foundations and implementation issues, to parody the subtitle of the book).

P.S.: I understand regulators wanting to improve the situation. There is an important item that they seems to ignore: transparency. Regulator are there to protect the public, not private interest. My request to regulators is that if they push for a new benchmark, the first point they have to ensure is that the benchmark is public information. All the historical data of the benchmark should be available publicly, without conditions, without fees and without registration. The data should be public as soon as available, no “insider information” is allowed, even for one minute. This does not seems to be the case for the moment.

If the regulators are ready to enforce the transparency and if they are willing to work with knowledgeable people (from the industry and academics) to analyze the direct and indirect impact of changes, I’m ready to support them. My contact details are available in the blog!

The graphs below represent the fixing of the two indexes over the last year and the a posteriori discount factors using the fixing (i.e. how much was required at those dates to get 1 USD today by investing overnight at the fixing).

Comparison between the Federal Fund Effective index and the General Collateral index.

A posteriori discount factor from the indicated dates to today (25 September 2014): Fed Fund vs GC.


Financial fiction: zero rate collateral

Episode 2: Zero rate collateral

There is certainly a push for more standardisation of financial products and their collateral terms – Credit Support Annexe (CSA) and margining process in particular. One particular discussion is around the CSA collateral remuneration and its equivalent Price Alignment Interest (PAI) used by Central Counterparts (CCPs). In the current standard terms an overnight rate (Fed Fund, EONIA, etc.) is paid in the currency of the trade in most cases. One potential solution to simplify the term of the CSAs, that I propose as my next fiction, would be to pay interest at a rate of 0 on the collateral. This would certainly simplify the computation of the interest part of any variation margin.

This proposal would align collateral and CCP process to the margin process used for exchange-traded futures. The amount paid as variation margin on futures, on OTC and on cleared trades would not include any interest any more and would be in line. As a secondary benefit, the overnight indexes fixing importance would have the role it should not have lost as an indicator of the economy and not as a main part of the economic process.

Suppose that there is a continuous perfect collateral, a collateral paid in cash in the currency of the instrument and a rate paid on the collateral of 0. From a valuation perspective, the valuation under collateral would become similar to the margining on futures: the difference of value with the previous valuation is exchanged and no interest is paid on that amount. The general futures price process theory, or the multi-curve and collateral framework as described in Chapter 8 of the book, both apply in this case.

What is the value of an Ibor coupon with CSA at rate 0? The answer in term of futures is easy (if we forget about notional and accrual factor)

PV0 = 1 - Φ0
with Φ0 the price of the STIR futures in 0.
Note that the fact that the coupon pays at the end of its actual period has no impact anymore on the valuation. The quote (to use the terminology of the book) is known at the fixing date of the Ibor index and from that date on, the required collateral is known and transferred. The payments in advance or in arrears have the same quote. Maybe there would be a legal distinction between the amount paid as collateral and the amount paid as coupon, but if we ignore that legal distinction, from a pure cash flow exchange perspective, everything is exchanged as soon as the cash flow is known; present value equals futures value (pun intended).

The general collateral principle is still valid: a promise to pay tomorrow is fulfilled by paying today the discounted forward value and adapting the amount up to the final payment. The difference here is the discounting is done at a rate of zero and the fact that no adaptation is required after the last fixing.
There is no convexity adjustment due to the difference in timing of the payments between futures and cleared swaps. This is a world where convexity adjustment becomes an exotic feature for non-standard collateral practice, not a vanilla characteristic of every curve calibration.

It is important to clarify that zero-rate collateral is not equivalent to zero collateral. The collateral is paid, there are cash-flows every day. The cash flow paid every day does not include any interest for previously paid cash flows. What has been paid is paid and we do not adjust the payment subsequently by added some interest to it. That may seems an extravagant proposal, not receiving interest on cash deposited. Looking at it from another point of view, in the futures market, which is probably the most liquid and oldest derivative financial market, used by banks, hedge funds, asset manager, pension funds, and corporates, nobody complains about the absence of PAI (or interest on previously paid profit). The usage of interest on collateral is more an habit (or maybe addiction?) than a fundamental economic necessity.

In interesting to note that the EONIA rate, which is computed in the afternoon of the starting date of the overnight period, is not publicly available anymore on a same day basis; it is available only on the next day. If a figure is used for general process and the regulator forces in some way market participants to use that process, the least we could hope from the regulator is to insure the minimal transparency and make sure the figures are publicly and fee-free available to all. To my opinion, this is a part of the "fixing scandal" that regulators have not addressed properly, if indexes are used for public processes, and anything mandatory by regulator rules should be considered as public, all the relevant related information should be public. The relevant information refers at the very least to the index value as soon as known and its full historical data. In the absence of public availability of the figures used currently, the proposal of a public and transparent rate a zero (0) would be a good improvement.


When fiction becomes reality

In one of my recent blogs, I proposed the first episode of a series in Finance Fiction. The blog presented packs and bundles options as an addition to the interest rate exchange-traded offering; it was based on ideas initially proposed in early 2013 in a paper on STIR futures and presented in Section 7.8.6 “Ceci nest pas une option” of the book.

It turns out that either someone read the paper and the blog and took it for reality or the ideas proposed were not so fictional. CME has announced it will start offering bundle futures(1) and bundle futures options from September 2014.

I’m not an expert in legal matters: Can an author claim copyright on reality when reality copies the author’s fiction?

The quote I used in the original paper on the subject (and in the book) was
Messieurs les Anglais, tirez les premiers !
Attributed by Voltaire to the (French) Comte d'Auteroche at the battle of Fontenoy, 1745
and I continued with
The XXIst century corporate warfare is probably not as courteous as the XVIIIth century real warfare and there will probably be no similar offer, but the question is open: who will shoot first?
Now we have the answer, the first to shoot are not English but American and they are based in Chicago.  USA did not exist as a nation when the Comte d'Auteroche spoke in 1745, so the absence of a similar offer to “Messieurs les Américains” is understandable.

Those new futures offer exposure to the same underlying Libor rates as the deliverable swap futures with same expiry and tenor. It seems that CME is creating competition for its own DSF through the new bundle futures. One of the reason for this apparent duplication is probably that in term of quotation mechanism and option strike the two instruments are quite different. The bundle futures contract is quoted in rate (more precisely 1-rate) and the current CME’s DSF contract is quoted in present value. The rate dimension is more familiar to the swap and STIR futures users, the present value dimension is more familiar to bond and bond futures users. Moreover the present value quoted DSF are not well suited for options on futures that would compete with swaptions.

Some of the points mentioned above may seems a little bit cryptic. The reason I'm not more explicit at this stage is that my thoughts on those points are the subjects of subsequent episodes of the Finance Fiction series. Any good series episode finishes with a teaser to the next episode, I don’t see any reason for not using the same technique here. The titles of some of the next episodes are:
  • Collateral with zero-rate
  • Risk based swap futures
  • Options on swap futures
In the last years, two of my fictions had a rapid turn-around into reality(2): the multi-curve framework initial paper was published in July 2007 and became the base of a standard in the subsequent crisis years; options on bundles (and packs) of STIR futures were proposed in March 2013 and will become an exchange-traded product in September 2014.

Given those precedents, I hope that some of my forthcoming fictions episodes will also become reality. If you are interested by my services related to future-proof futures design, I’m available for consulting :)

(1) Bundle futures is a new term invented by CME for the occasion. It is financially equivalent to bundles on futures but a bundle futures is traded as unique contract and deliver into the underlying individual STIR futures only on expiry.

(2) For obvious marketing reasons, I do not highlight the proposals that failed to materialise, like options on composition or OIS swaption.

Financial fiction: Pack's option

Finance fiction

After numerous conferences on the impact of regulation and the new market structure on quantitative finance, it’s time to start thinking about the impact the quants can have on regulation and the market structure.

The book not only covers theoretical considerations about the foundations of a multi-curve framework, and practical considerations about liquid instruments, it also contains directly or indirectly some "finance fiction" episodes where non-existent instruments or practices are described.

The reason to introduce such fictions in a non-fiction book is that the market is changing and is largely incomplete. Instruments that were completely redundant in the past are now becoming nice-to-haves or even must-haves. Changes in regulatory treatment, movement to futurization, generalisation of collateral and margining practices have created a moving ground. The financial landscape is moving; I try to guess some of the potential new characters.

After speaking at numerous conferences where the topic was something like "impact of the crisis/regulation on quantitative finance", I would like to start a new trend on "impact of quants on regulation/market structure". The indirect goal of those episodes is to influence changes in the direction of a more complete offering or simpler rules.

My first episode in that trend is:

Episode 1: Pack's options

Packs and bundles

A futures pack is a block of four consecutive STIR futures (1st to 4th, 5th to 8th, etc.). The packs are colour-coded, from the first to the tenth pack: white, red, green, blue, gold, purple, orange, pink, silver, and copper. The packs are traded as such on different exchanges; one trade creates positions in the four underlying futures. A futures bundle is a block of the first packs. A n-year bundle is a block of the first n packs, i.e. the block of the 4*n first futures.

Packs and bundles are traded on CME in USD and on LIFFE (and planned at NLX) in EUR and GBP.

A single futures contract is the exchange-traded equivalent of the OTC FRA; a pack is the equivalent (in terms of Ibor fixing involved) of a one year forward starting swap; and a bundle is the equivalent of a n-year spot starting swap.

Ceci n'est pas une option

New options on STIR futures have been added recently to the offering with mid-curve options now offered up to five years. Nevertheless the offering is still in some way incomplete. A single futures contract is equivalent to a FRA, a pack/bundle is equivalent to a swap. On the option side, an option on a future is the exchange-traded equivalent of the OTC caplet or floorlet. But where are the equivalents of swaptions and forward starting swaptions? This is certainly a missing instrument in the exchange-traded offering(1). It is not an option for traders to trade the equivalent of swaptions in the futures world.

Ceci n'est pas une pipe.
La trahison des images, René Magritte, 1928.

New option

Completing the missing offering could be achieved in different ways. Our suggestion for this episode is to create options on packs and options on bundles. To our knowledge none of these products are currently offered at any exchange. Given the push for more standardisation and exchange-traded products, the question is which exchange will be the first to offer such a product?

Messieurs les Anglais, tirez les premiers !
Attributed by Voltaire to the (French) Comte d'Auteroche at the battle of Fontenoy, 1745

The XXI century corporate warfare is probably not as courteous as the XVIII century real warfare, and there will probably be no similar offer, but the question remains open: who will shoot first?

What are the details of those options?

The options are characterized by an expiry date and a strike (denoted K below). The option is on a given pack or bundle (with n futures in the block) and can be of the call or put type. The option could be traded on a premium or continuous margin basis. As I personally prefer the margined options for futures, I describe here only the margined version. The options are traded in price(2). A settlement/closing price is computed every day by the exchange; usually it represents the price at the end of the trading period. The profit (today's price minus yesterday's price) is paid immediately by the short party to the long party (obviously if the numbers computed are negative, in practice the positive flow takes place in the opposite direction). This is a usual futures-style margin process.

On the expiry date, the call (resp. put) long party has the right (but not the obligation) to enter into a long (resp. short) position in the n futures underlying the pack/bundle. This is an all-or-nothing option; the exercise is for all the futures in the block; the exercising party cannot select which futures in the block are exercised and which are not. The futures exercised are obviously fungible with standard STIR futures. The price at which the futures are entered into is the same for all of them in the block and is K.

If we denote by Fi the price of the i-th future in the block, the pay-off can be written as
Sumi=1n (Fi- K)

Why a new product?

Given the inertia around any new product, especially in very standardised settings, we need a compelling reason for a new product.

Let me start with the non-compelling reasons. Those reasons are technical. The existence of a larger class of options, i.e. adding a pack's options to the futures, vanilla options and mid-curve options will enrich the calibrating instruments of models. This is important to price exotic options that depend on the correlation structure between LIBORs at different dates. Currently those options are not represented in the exchange-traded world.

But who needs exotics today?, I hear you ask. My answer is that new regulations are imposing exotic structures to standard products, like some path dependent caps and floors on mortgages, or timing adjustment on rolled deposits (LTRO), etc. One has to define "exotic": in the sense used here, it is not related to liquidity but a technical term meaning we need a dynamic model and a non-trivial numerical procedure to solve it. Enter into this category a lot of liquid products: bond futures (delivery option), FRA (FRA discounting), and change of collateral/margin. A lot of liquid products are, in the sense used here, exotic products.

The main reason for creating the new product is to fill a gap. The interest rate option market is important as very popular types of mortgages are fixed rate prepayable (the borrower has the option to repay his mortgage) or floating rate with some kind of cap/floor (potentially path dependent). A liquid exchange-traded market for options is useful. Currently that market exists only partially. Options on STIR futures are very short-term options of the cap/floor type, mid-curve options extend to underlying up to 5 years but are also very short-term expiry and on specific rates, not on a block of them. Offering options on packs and bundles would give more flexibility for hedging and expressing views. Options on bundles would be similar to swaptions and options on packs would be similar to options on forward starting swaps. The swaptions are the most liquid interest rate options in the OTC world. The reason of the liquid market on swaptions is also valid for a liquid market on the pack's options.

STIR futures are offered only to 10 years, with a lot less liquidity above 5 years. The interest on the pack's options would be mainly on the short to medium term sectors. For options on long-term rates (up to 30 years and maybe 50 years), another product would be required. But discussing that issue requires multiple new episodes, one for a "clean" swap future and one for the options on them.

And the pricing?

A technical discussion on how to price options on packs and bundles in a stochastic basis model is proposed in the book (Chapter 7, Section 8). In summary, in a Gaussian one-factor HJM with simple stochastic spread, the approaches used for swaptions and STIR futures with stochastic spread can be combined. If the products are becoming liquid, a model with smile dynamic would need to be developed, but that would be a non-fiction episode conditional to the realisation of the fiction.

(1) Some options on swap futures exist, but they are mostly illiquid. Some options on deliverable swap futures (DSF) may be added in the future, but for this the creation of a "clean DSF" is required. That in itself is another finance fiction episode.

(2) The term price for (options on) futures is a misnomer as the price is never paid; a term like "reference index" would be a better name. See also the introduction of Chapter 8 in the book for more on the subject.

Edit (13 August 2014): A slightly modified version of this blog appeared on OpenGamma's blog under the title: The Impact of Quants on Regulation and Market Structure.


Course on multi-curve and collateral framework

Since 2007, a new framework has become the standard for interest rate derivative pricing: the multi-curve framework (also called multiple curve). Another market reality has gained more importance: the collateralization of interbank trades.

Even if the frameworks for multi-curves and collateral are nowadays relatively standard, their details and the far-reaching impacts of seemingly small changes are not always fully understood. Over the past few years, I've written several papers on these frameworks and published a book. I have also been one of the architects of a very flexible and efficient open source implementation of those frameworks. It can be found at http://strata.opengamma.io/

Writing technical papers and the code is not an end in itself, as people not only want to know the minutia of the associated mathematics and read the detailed code, but they also want to see the big picture, how it is used in practice, see examples in spreadsheet format, understand what are the impacts and see what is still missing. Reading a collection of unrelated papers with different notations found on internet is not always the most efficient way to get there. To discuss all those details, the best way is often the good old way of listening to a human being in a course or workshop.

Over the last years I presented several of such courses in different formats. It has been presented as a 15-hour course in the master program of University College London where I’m a visiting professor; as a one-day workshop in several WBS conferences; and as in-house training for several banks.
As I have received more questions about this type of course, I have been very systematic at preparing detailed slides, writing a extended agenda, cleaning lecture notes, putting together detailed spreadsheets linked to a production-grade implementation, etc.

I have collected the summary and a typical agenda; they can be found below. Obviously if you are interested in such a course, don’t hesitate to contact me.

Multi-curve framework

  • Definitions and fundamental hypothesis of the framework. The basic instruments. The multi-curve framework is based on relatively simple hypothesis, but those hypothesis are far reaching with subtle impacts.
  • Curve description: Defining flexible curves. Spread curves. What to interpolate? Impact of interpolation on risk.
  • Curve calibration: 
    •  Standard curves or simultaneous calibration. The multi-curve framework is more than a juxtaposition of single curves. The curves interacts and calibrating them simultaneously is often required. The basis swaps have also an impact on how to look at risk. Several markets have idiosyncrasies that need to be taken into account: two-swaps basis swaps in EUR, Fed Funds swaps in USD, change of frequency for AUD IRS, 
    • Curve are never simple. Incorporating turn-of-year, central bank meeting dates, dealing with sparse data, 
    • Risk computation: the growing number of (delta) risk figures. With multiple curves, the number of risk factors is also multiplied. How to look at risks for (linear) products?
    • Jacobian/transition matrices.
    • The market quotes are quite heterogeneous in term of instrument used and tenors. Standardisation of nodes and remapping of risk make it easier to read reports. It can also be used to store/use historical data for VaR, scenarios, statistical analysis. The synthetic curves.
  • Other instruments. The pricing curves have multiplied but the number of liquid instruments has not increased in the same way. The information need to be found where it is, and that includes using different instruments for curve construction and have them in the books for hedging: STIR futures, Fed Funds swaps, Deliverable Swap Futures (CME), Libor coupons with compounding (CAD but also basis swaps), Fed Funds futures, 
  • Modelling stochastic basis spread. The impact of the crisis is not only differentiated curves but also moving spread between them. What is the impact of those stochastic spread on vanilla instruments?
  • Impact of multi-curve framework on interest rate modelling. The standard pre-crisis models have been developed for one (risk-free discounting) curve. How to extend them relatively simply to the multi-curve framework? Black and SABR models in multi-curve. HJM/LMM.
  • Efficient computation of risk (algorithmic differentiation). The increasing number of market quotes used to build curves is not only a challenge for users (risk managers and traders) but also for efficient computation. A single currency vanilla instruments will often have 100 bucketed risk nodes. Algorithmic differentiation is a powerful tool that has been used for a long time in engineering and has made its way to finance in the last 5 years. How efficient is it for curve calibration and risk computation of interest rate books? Impact of multi-curve on quantitative finance library architecture.


  • Cash collateral and generalization. The cash-collateral discounting approach has been around for a couple of years now. The standard results and their exact application. Extension to generalized definitions of collateral. What is hidden behind OIS discounting (and when it can not be used).
  • Assets (bonds) collateral. Not all CSA/collateral agreements are based on cash. Generalization of collateral results for collateral with assets (collateral square).
  • Foreign currency collateral. Impact of foreign currency cash collateral.
  • Multi-curve and collateral. Most of the collateral literature focuses on the ``discounting'' aspect of collateral. Description of a joint multi-curve and collateral framework.
  • Clearing houses (CCP). Cleared swaps and collateral.
  • Collateral adjusted curve calibration. Extending the curve calibration for multiple collateral.
  • Modelling with collateral. Models very similar to the HJM model can be developed with collateral discounting. Even if they are similar to the old HJM, the collateral adds an extra layer of complexity and an extra layer of spreads to deal with. Modelling, even simple instruments like STIR futures, in that set-up is a challenge.
  • Convexity adjustment for change of collateral. There is not yet a consensus on how to compute convexity adjustment for change of collateral (foreign currency in particular). In some special cases, some estimation can be obtained.
  • Risk in multiple collateral environment. Even if all the change of collateral adjustments are not computed, their concentration of risks can be reported.

Edited several times. Last edit: 29 October 2016.



The multi-curve framework book is now the
#1 Amazon bestseller
category Business, Finance & Law > Professional Finance > Interest


Multi-curve and golf

Golf is multi-curve: draw, fade, breaking puts, good and bad bounces, back spin, slice, hook, etc.

As a lot of you know, I'm a keen golfer. When I'm not dreaming the solution to all problems about multi-curve (see page xii of the book for more on that), I'm dreaming about birdies (eagles will be for next year :) ).

I have ordered some swag golf balls with the book title as logo (see picture below). Obviously those balls are for grab. If you are a reader of the multi-curve book, want to play a round of golf, just let me know. I will be happy to offer a multi-curve ball (Pro V1x - 2014) to any reader I meet on the tee.

When I'm not writing or coding about the multi-curve framework, I can be found on different courses around London and Brussels; I will be glad to discover new ones. Don't hesitate to challenge me for a round.
Golf balls with Multi-curve Framework logo resting on a Multi-curve Framework book.

Endorsement: Daminano Brigo and Andrea Pallavicini

This is an important and much needed book looking at multiple interest rate curves, including collateralization. The subject is introduced motivating all developments from a historical perspective and is very pleasant to read. Both a rigorous theoretical approach and detailed practical recipes for bootstrapping and interpolation techniques are provided, in a coordinated fashion, using real market products. Advanced discussion of multiple curve dynamics, with specific modeling choices, is also given in the final part. From one of the originators and protagonists of the recent multiple curves literature, this is an appealing book for a potentially wide audience and is strongly recommended.

Prof Damiano Brigo
Dept of Mathematics, Imperial College London, and Director of the Capco institute, and
Dr Andrea Pallavicini
Imperial College London and Head of Equity, Fx and Commodities models, Banca IMI


Endorsement: Chyng Wen Tee

As you have seen on the book's cover, Professor Chyng Wen Tee (Assistant Professor of Quantitative Finance, Singapore Management University) was kind enough to endorse the book.

The endorsement printed on the back cover was not the full original text of the endorsement; the original endorsement was longer and would not have fit on the back cover.

The full original text:
As a quantitative finance practitioner-turned-academic, I read Dr. Henrard's Interest Rate Modelling in the Multi-curve Framework with great interest and excitement. Seven years after the onset of the infamous financial crisis that started in 2007, credible reference textbooks refurbishing our approach to interest rate modelling remain sparse, leading to a dichotomous gap between the interest rate models taught in a university and the interest rate models applied in practice. In the academic world, all too often the teaching of important concepts about time value of money, discounting and forwarding becomes commingled under the single-curve framework. Students consequently lose context, and graduate with only a loose understanding of the key concepts, without grasping the essence and salient points of interest rate models. On the other hand, from a practitioner's perspective, while numerous leading investment banks have since rolled out a multi-curve interest rate pricing architecture, a good rigorous reference textbook laying out the theoretical foundation and filling in the necessary mathematics with germane rigour is still lacking.

This book provides all the vital missing links for academic and practitioners alike, effectively bridging the gap between theory and practice. Unlike many textbooks which only focus on theory, Dr. Henrard's book takes a unique bottom up approach, guiding the reader all the way from the formulation of fundamental mathematical framework to actual implementation in a production environment, delving along the way into advanced topics including collateralisation, multi-curve calibration, implication on portfolio management as well as exposition on a wealth of interest rate products. This book more than delivers what it promises as far as foundations, evolution and implementation go. Dr. Henrard's elucidating and engaging writing style makes this highly informative book a pleasure to read. On top of that, this a book that also furnishes you with intuition, perspectives and a solid understanding of what forward rates and discount factors really mean. There's little doubt that this will be the de facto textbook on interest rate modelling for many years to come.
Prof. Chyng Wen Tee
Assistant Professor of Quantitative Finance, Singapore Management University


Endorsement: Stéphane Crépey

As you have seen on the book's cover, Professor Stéphane Crépey (Head of Probability and Mathematical Finance, University of Every, France) was kind enough to endorse the book.

The endorsement printed on the back cover was not the full original text of the endorsement; it was a little bit longer and contained some comments to start a dialogue or debate on some philosophical questions about the multi-curve framework.

The full original text:

With his two seminal ''irony'' papers, Marc Henrard is one of the very first to have identified (and in fact, anticipated) the importance of the interest rate multi-curve tsunami that came in the aftermath of the global financial crisis. Quite logically, this is also the focus of his book, one of the very few of its kind. Indeed, "competitors" typically also (and mainly) deal with CVA, FVA and the likes, so that there is usually not much space left for the multi-curve issue per se. By contrast, Marc addresses the question from foundations to curve calibration (a must read in the book). I’m not so sure about the statement that ‘the framework is different from the previous one-curve approach in fundamental aspects’, but in a sense this is a matter of point of view. All together, a very practical and nice read.
Oh, by the way, ''What is the present value of an FRA?''

Professor Stéphane Crépey
Head of Probability and Mathematical Finance, University of Every, France


The picture on the book's cover: the story behind it.

The picture used as background for this blog is also the one used on the book's cover. It may look like a set of greenish color bands, but it is more than that. The picture used on the cover is not the most important part of the book (if it is for you, maybe I have missed my goal writing the book). Nevertheless there is a small story behind it and I though it was worth sharing it.

The initial book jacket proposal from the editor was not really to my taste. At the time the editor didn't want to change the collection cover. I made a couple of suggestions to change the small color square on the original design using some of the pictures in my personal library. A couple of weeks before the publication date for the book, to my surprise (and joy), the editor decided to change completely the design for the entire collection. For my book, which is the first with the new design, he used one of the pictures I had suggested, the one you can see on the blog background. The picture is simply the close-up of a palm-tree leave. It is a "natural" picture. The other books in the collection will use computer generated pictures with geometrical figures.

When my Mum saw the book cover for the first time, she said that it looked like a "botanical book". As you know from the story of the cover picture, this is a true statement, in some sense of the term "botanical".
La mathématique est l’art de donner le même nom à des choses différentes.

Henri Poincaré.

Personal translation: Mathematics is the art of giving the same name to different items.

My Belgium house, the place from where I write most of my articles, is located in the region of Brussels (technically it is not located in the municipality of Brussels, which is only one of the 19 municipalities composing Brussels region, but I don't want to bore you with Belgian political system). The precise location is unimportant, except that it is located just next to the "Jardin Botanique", i.e. the botanical garden of Brussels. So even if the picture on the cover was not taken in that botanical garden, my links to botanical science extend not only to the cover of my book but also to the location where it was mainly written.

I have to add a third botanical connection. My grand fathers were both agronomist. They worked most of their careers in what was then the "Belgian Congo". Looking at books in the familly library, I can find books like "L'Arboretum de Stanleyville" and "Reforestation sur grande échelle au Kivu", written by my grand father Paul Liégeois in the 50s. So certainly a family connection to trees (not of the binomial/trinomial type but of the wood type) and leaves.

Book's cover

Sample chapter

A sample chapter, the table of content and the index of the book are now available on the Palgrave website.

The sample chapter is the long introduction (10 pages); it is an introduction to the book but also to the history of the multi-curve framework.

The book page on Palgrave site is: http://www.palgrave.com/products/title.aspx?pid=707837

The sample chapter can be found at: http://www.palgrave.com/resources/sample-chapters/9781137374653_sample.pdf


How it came to life.

The first lines of the book were written in 2006. At the time the term multi-curve framework, which is used for the book's title, had not been coined and my idea was only to write a couple of pages for a note. In the mean time, August 2007 changed the course of writing on interest rate curve modelling for ever.
Festina lente.
Latin saying
Personal translation: Haste slowly.

The starting point of the reflection was my quest to answer the question ``What is the present value of a FRA?'' in a way that convinces me. The initial intend was a personal quest to understand the foundation of a fundamental, and in appearance simple, quantitative finance question. I could not find an answer in the literature satisfactory to me. The answers I could find were either ``it is trivial'', i.e. ``don't ask silly questions'', either a description of a replication argument for which it was not acceptable to discuss the numerous hidden hypothesis. Discussing the hypothesis was not politically correct as a scientist and as a business manager. For the former, it questioned a foundation of quantitative finance, and thus the developments build on those foundations. For the latter, it was not seen positively by executive committee members, board members and supervisors as it casted doubts on official accounting figures - maybe rightly so - and had legal implications; it was not acceptable to say that official figures were "fishy" or even simply uncertain.

Ironically, the first article to come out of those reflections, titled The Irony in derivatives discounting, was published just one month before the now famous August 2007. The publication was not a prediction of what would happen in the derivative market just after and should not be seen as a premonition. Neither should it be seen as a cause of the crisis. It was nevertheless an indication of inconsistencies in the practice of derivative pricing that were not answered by a coherent theoretical framework.

The book, which started, unbeknown to its author, seven years ago, is intended to be a description of the current status of the subject, which is now called the multi-curve framework. It borrows from the developments of numerous practitioners and academics working on the subject. The length of the bibliography, with most of the references dating from 2009 and after, is a witness of the activity on the subject over the last years.

Hopefully the reader will find as much interest in the subject as I have over the last eight years. Hopefully he will also be intrigued, surprised, amused and maybe amazed at some of the subject facets.

Oh, by the way, my quest is still on! I'm still asking myself ``What is the present value of a FRA?'', even if the question has changed to ``What is the collateral quote of a FRA?'' (read the book for the meaning behind the new question ;) ). A question source of insomnia ... and maybe the starting point of another book in a couple of years.


P.S. This post is largely inspired by the book preface.


It's here!

Advance copies of my new book "Interest Rate Modelling in the Multi-curve Framework: Foundations, Evolution, and Implementation" just arrived from the printer. Copies will be available at the Bachelier World Congress in Brussels (2-5 June, 2014).

More information will be posted in the coming days.

Any author will tell you that writing a book is a wonderful journey. Actually no, the wonderful journey was to dream it!

Chacun sa méthode... Moi, je travaille en dormant et la solution de tous les problèmes, je la trouve en rêvant.
Drôle de drame (1937) - Marcel Carné

Personal translation: Each his own method . . . Myself, I work sleeping and the solution to all problems, I find it dreaming.