**Multi-curve and collateral framework: foundations, evolution and implementation.****The future of LIBOR: Quantitative perspective on benchmarks, overnight, fallback and regulation.****Algorithmic Differentiation in Finance****Central clearing and bilateral margin**

*Agenda tailored to your needs.*

*Detailed lecture notes.*

*Associated to open source code for practical implementation.*

*Training in English or French*

#
Multi-curve and collateral framework:

foundations, evolution and implementation.

### 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 have 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 interbank 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 new 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 multiplication 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 Agenda:

**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.

**Collateral**

- 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.

#
**The future of LIBOR: **

Quantitative perspective on benchmarks, overnight, fallback and regulation.

Quantitative perspective on benchmarks, overnight, fallback and regulation.

### Typical Course Agenda:

- EU Benchmark regulation
- The "alternative" benchmarks
- SOFR, reformed SONIA, ESTER, SARON, TONAR
- Secured v unsecured choice
- What about term rates?
- Curve calibration
- SOFR and EFFR: two overnight rates in one currency!
- Status in different currencies. Cleared OTC products, liquidity. The different consultations in progress and what to expect from them.
- Fallback procedure
- ISDA consultation
- The different options for the "
*adjusted rate*" - The different options for the "
*adjustment spread*" - Quantitative impacts: convexity adjustments and risk
- Clearing house adoption
- New products associated to new benchmarks
- Futures on overnight benchmarks
- Deliverable swap futures

Detailed lecture notes provided to participants.

Tools to measure the impact in term of risk and valuation on swap portfolios available.

#
**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:

- 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**

- Clearing/variation margin/initial margin regulatory time table
- Valuation under (variation margin) collateral: Overnight rate collateral, Foreign currency collateral, Bonds collateral
- What information about change of collateral is available in the market?
- Risk management of interest rate risk with foreign currency collateral
- CCP initial margin methodologies: LCH, CME, Eurex
- Bilateral margin: regulatory requirement / ISDA(R) SIMM proposal
- Cost of clearing: fees, capital, CVA, default funds, MVA / Cost of not clearing
- Capital consideration for clearing and bilateral trades - CEM, SA-CCR
- Multiple clearing houses / local clearing houses / LCH-CME and LCH-Eurex basis

## 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.

### 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. 2018*Regulation, Collateral, and Multi-curve dynamic*. Bank in South-Africa. 2018