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.

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