We propose in-house training and workshops on subjects related to quantitative finance and risk management.

We offer extensive flexibility on the training organization.

A in-house tailor-made course with our experts presented to your full team often cost less than sending two people to a standard course organized by a large training firm.

Agenda tailored to your needs. Detailed lecture notes.
Associated to open source code for practical implementation.
Training in English or French

We are an (fiercely) independent management owned advisory firm and the trainings reflect that independence. We don't have hidden agenda and are free of conflict of interest.

In the current situation, we are also happy to offer virtual/on-line courses/workshop. The configuration is even more flexible that in-person courses as participants in different locations can attend simultaneously and courses can be split in half days to avoid participants lassitude.

Some of the popular courses are:
  1. Multi-curve and collateral framework: foundations, evolution and implementation.
  2. Benchmarks in transition: Quantitative perspective on benchmarks, transition, fallback and regulation.
  3. Algorithmic Differentiation in Finance
  4. Central clearing and bilateral margin

Multi-curve and collateral framework:
foundations, evolution and implementation.

Introduction (by Marc)

Over the past 10 years, I have written many papers on the multi-curve framework and published a book on the subject. I have also been one of the architects of a very flexible and efficient open source implementation which can be found at

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 human readable 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 interacting with a human being in a course or workshop format.

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 or two-day workshops with several training providers, 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 an extended agenda, cleaning lecture notes, putting together detailed spreadsheets linked to a production-grade implementation, etc.

Course summary

Interest rate modelling has changed dramatically since the financial crisis start in 2007. Most of the models used in academic literature and by practitioners had to be reviewed with those changes in mind. Another market reality has gained more importance and became the de facto market standard with the new regulation that came into effect on 1st March 2017: the collateralization of derivatives trades. The course describes in details those two related major changes that are the adoption of the multi-curve framework and the collateral framework.

The multi-curve framework is a way to describe coherently a market where basis swaps, exchanging payments linked to different indices, require a spread. Not all the indices are equal, and each index requires its own curve. Nevertheless, the curves cannot be created indiscriminately if one wants to maintain a coherent approach.

The course details the foundations of this approach. It has been adopted as the new standard by most financial institutions. We analyse the impact on the interaction between the curves, how market instrument liquidity and conventions force curves that are a lot more than simply a collection of single curves. A very generic curve calibration process, adapted to the multi-curve framework, is described. Even if the frameworks for multi-curve is nowadays relatively standard, their details and the far-reaching impacts of seemingly small changes are not always fully understood.

Constructing multiple curves is only a small part of the game in practice. The real challenge is to use them to hedge portfolios, describe risks coherently and link them to complex interest rate models built originally in the single-curve framework. The foundations of those links and extensions are proposed, based on the most recent literature.

The other side of changes in the market is the emphasis on collateralization and its impact on derivative pricing. Part of the course is devoted to the extension of the multi-curve framework in presence of collateral. In particular the so-called "OIS discounting" pricing is analysed in detail, including its often hidden hypothesis. The collateral pricing is at the same time a very robust framework when all the ingredients are there but very fragile when you try to create it or want to change some ingredients. This is a very important aspect that need to be kept in mind when trying to reform part of the system.

The lecture notes of the workshop are provided in the form of the book Interest Rate Modelling in the Multi-Curve Framework: Foundations, Evolution and Implementation, Palgrave (2014).

Typical Course Content (1 day or 2 days)


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.
  • New regulation related to collateral. Variation margin and initial margin.
  • 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.
  • Risk in multiple collateral environment. Even if all the change of collateral adjustments are not computed, their concentration of risks can be reported.

Benchmarks in transition:
Quantitative perspective on benchmarks, transition, fallback and regulation.

With the increased expectation of some IBORs discontinuation, the overnight benchmark changes and the increasing regulatory requirements related to benchmarks, a clear quantitative finance perspective on the impacts for derivatives is becoming paramount.

The recent regulations include the mandatory Variation Margin (VM) and the EU Benchmark Regulation (BMR). VM and the related remuneration of collateral means that overnight benchmarks are now ubiquitous. The EU BMR will have severe impacts on derivative market from January 2022. For all major currencies, new benchmarks have been proposed and the markets are in a transition phase. Each transition has its own idiosyncrasies and a common transition approach cannot be expected. On the EUR side, a recalibration approach with clean discounting has been introduced for EONIA to ESTR transition since 2 October 2019. On the USD side, two overnight benchmarks exists in parallel: SOFR and EFFR. The existence of multiple overnight benchmarks generate not only discounting adjustments but also "convexity" adjustments between similar instruments with different collateral rules.

Regarding IBOR fallbacks the "compounding setting in arrears with 2 days shift" adjusted rate and the "historical median spread with a 5-year look-back period" have been selected. The historical approach has created and still creates value transfer. The overnight compounding in arrears change significantly the risk profile of the legacy instruments. Moreover the instruments generated by the fallback are not OIS-like and have hidden unmanageable risks. At the same time new instruments are created on the new benchmarks while the liquidity associated to them is progressing at different speeds in different currencies. Those new benchmarks are themselves in competition with new comers like AMERIBOR, term rates or Bank Yield Index.

In the course, all those issues are presented in detail, based on quantitative finance analysis. Historical data is used to illustrate the impacts. All the aspects presented have been implemented in production grade libraries by the lecturer and the analysis is based on those implementations.

The course can be followed by actual "what-if" analysis of the different elements on the actual large scale portfolio of the clients or on test portfolios.

Typical Course Agenda - 1 day course:

  • Cash-collateral discounting and overnight benchmarks
    • The standard collateral results and their exact application
    • What is hidden behind OIS discounting (and when it cannot be used)?
  • Overnight Benchmark Transition
    • Progress in different jurisdictions
    • EFFR and SOFR: two overnight rates in one currency! Differences and transition.
    • EONIA and ESTR: recalibration and transition
    • SOFR intra-month seasonality: Curve calibration impacts
    • Implicit convexity adjustments
    • Results from the Collateral and discounting transition at CCPs
  • Brief history of LIBOR
    • History
    • Volumes
    • EU/UK BMR
  • IBOR Fallback procedure
    • ISDA proposal and definitions
    • Adjusted RFR: compounding setting in arrears
    • Term rates: a credible alternative?
    • The adjustment spread: historical median approach
    • Historical data associated to the spread computation
    • Value transfer: transfers already incorporated and transfers to come
    • Change of term sheet in existing vanilla instruments
    • Presenting the fallback in the language of quantitative finance
    • Implicit convexity adjustments
    • ICE Swap Rate fallback
    • Fallback for ED futures and options
  • Risk management of transition
    • Delta risk through the transition
    • Fallback gaps and overlaps
    • Potential impacts on systems
    • Multi-curve: double or quit?
    • Vanilla becoming exotics: cap/floor and swaptions
    • Value transfer and arbitrage opportunities
    • Alternative to ISDA protocol
    • Valuing derivatives in a two collateral world
  • Clearing house adoption
    • Differences between bilateral and CCP rules
    • Fallback adoptions (or not), CCP divergence from ISDA definitions
    • Valuation of legacy uncleared swaps, cost of signing the protocol
  • New products associated to new benchmarks
    • Futures on overnight benchmarks
    • Deliverable swap futures
    • Bond/loan conventions

Follow-up: hand-on workshops

Practical implementation of several of the issues discussed in the course. Each subject can take between one hour and one day, depending on the level of details and the actual implementation in the client systems.

  • Computation of historical spreads (LIBOR - compounding in arrears) for the different currencies and tenors.
  • Detailed analysis and pricing of the cashflow resulting from the IBOR fallback. Cashflows are associated to overnight in arrears but are significantly different from a clean OIS. Pricing and risk management of those cashflows present unique chalenges with spikes of exposure.
  • Convexity adjustments from change of collateral: discounting, IBOR forward, OIS forwards, option valuation (including swaption valuation).
  • Curve calibration: including two overnight rates and the IBOR fallback.
  • Bilateral CSA transition. Transition from one overnight rate to another. Incorporating delivery options and bond VM in valuation.

Algorithmic Differentiation in Finance

Course summary:

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.

The lecture notes of the workshop are provided in the form of the recently published book Algorithmic Differentiation in Finance Explained, Palgrave (2017).

The workshop is backed by open source code (freely available on Github). On one side, the code is composed of tutorials of increased complexity. Those tutorials present the different fundamental principles of AD and propose several implementation for each of them. Another side of the code used is a full production grade quantitative finance library using AD as one of its tools. That library is used in production by hedge funds, banks and clearing houses.

Learning outcomes:

The mathematical foundations of Algorithmic Differentiation methods.
The effective application and use of AD in finance.
Beyond vanilla implementation: further efficiency gains specific to finance.

Typical Course Agenda - 1 day course:

  • Introduction
    • AD is magic (or not)!
    • Exact derivatives
    • Finite difference
    • Development time v running time
  • The Principles of Algorithmic Differentiation
    • Derivative
    • Composition
    • Algorithm: assignment
    • Algorithm: branches
    • Algorithm: loops
  • Application to Finance
    • Basics: Black formula and SABR
    • Interest rate sensitivities
    • Monte Carlo
  • Automatic Algorithmic Differentiation
    • Standard Algorithmic Differentiation by Operator Overloading
    • Adjoint Algorithmic Differentiation by Operator Overloading
    • Automatic Algorithmic Differentiation applied to finance
    • Mixed Algorithmic Differentiation implementations
  • Application to Finance (2)
    • Automatic Algorithmic Differentiation applied to finance
    • Non-derivatives with respect to inputs - sticky smile
  • Calibration
    • Curve calibration
    • Model calibration and implicit function theorem: exact calibration
    • Model calibration: least-square

Central clearing and bilateral margin

One day course.
  • Clearing/variation margin/initial margin regulatory time table
  • Valuation under (variation margin) collateral: Overnight rate collateral, Foreign currency collateral, Bonds collateral
  • Risk management of interest rate risk with foreign currency collateral
  • CCP initial margin methodologies: LCH, CME, Eurex
  • Bilateral initial margin methodologies: UMR regulatory requirement and ISDA(R) SIMM approach
  • Cost of clearing: valuation including initial margin - MVA
  • Margin reduction: non-cleared legacy, non-cleared UMR and cleared
  • Multiple clearing houses: market fragmentation and basis: CME/Eurex/JSCC/LCH
  • Discounting transition big-bang (EUR ESTR and USD SOFR)
  • CCP and LIBOR fallback

Recent training

Public workshops

  • Workshop Multi-curve and collateral framework. One day workshop at The 10th Fixed Income Conference (Barcelona, Spain), September 2014.
  • Workshop Valuation and Risk Management in the Margin Paradigm. Two days workshop. (Warsaw, Poland), December 2015.
  • Workshop OTC margin and the true cost of clearing. One day workshop (London, UK), 23 February 2016.
  • Workshop Collateral, regulation and multi-curve. Belfius Financial Engineering Fund Workshop at KUL/Leuven University (Leuven, Belgium), December 2017.
  • Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (London, UK), September 2018.
  • Workshop The future of LIBOR: Quantitative perspective on benchmarks, overnight, fallback and regulation. Finans Foreningen workshop (Copenhagen, Denmark), 24 January 2019.
  • Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (New York, U.S.A.), March 2019.
  • Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (Singapore), April 2019.
  • Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (London, UK), April 2019.
  • Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (London, UK), September 2019.
  • Workshop The future of LIBOR: Quantitative perspective on benchmarks, transition, fallback and regulation. WBS Quantitative Finance Conference (Italy, Rome), 16 October 2019.
  • Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (Singapore), November 2019.
  • Workshop LIBOR transition: Quantitative perspective on benchmarks, transition, fallback and regulation. RiskMinds (Amsterdam, The Netherlands), 6 December 2019. 
  • Workshop Rate reform: Quantitative perspective on benchmarks, transition, fallback and regulation. WBS Interest Rate Reform Conference (A Quant Perspective) (London, UK), 4 March 2020.
  • Planned: Benchmarks in transition: Quantitative perspective on benchmarks, transition, fallback and regulation. QuantMinds International, KNect365 (Hamburg, Germany), 12-14 May 2020 / postponed to November 2020.
  • Planned: Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (London, UK), April 2020.
  • Planned: Interest Rate Modelling in the Multi-curve Framework: Collateral and Regulatory Requirements. LFS Workshop (Singapore), May 2010.

In-house training

  • Valuation and Risk Management with Variation Margin and Initial Margin. Bank in New-York. 2016 
  • Quantitative impact of margin regulatory requirements. Hedge fund in New-York, 2016.
  • Asymmetric variation margin. International financial institution in Europe, 2018.
  • Regulation, Collateral, and Multi-curve dynamic. Bank in South-Africa, 2018.
  • The future of LIBOR: a quantitative perspective. Bank in Belgium, 2019.
  • LIBOR transition and fallback: Uncleared versus cleared. Consulting firm in Belgium, 2019.