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Course Calendar Course Calendar

Interest Rate Modelling

Day One

Pricing with Collateral – Variation Margin

  • Margin: terminology, fundamentals and market infrastructure
  • Regulatory framework for Variation Margin, CSA, time table
  • Cash collateral and generalization. The cash-collateral discounting. The standard collateral results and their exact application. Extension to generalized definitions of collateral. What is hidden behind OIS discounting (and when it cannot 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 on valuation

Multi-curve Framework

  • Definitions and fundamental hypothesis of the framework. The relation to collateral. The basic instruments. The multi-curve framework is based on relatively simple hypothesis, but those hypotheses 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 interact 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 
    • Curves are never simple. Incorporating turn-of-year, central bank meeting dates and 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. Standardization 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 and statistical analysis
  • Risk management in a multi-curve/multi-currency framework


  • Changes in benchmarks. Changes are expected for the main benchmarks – like LIBOR – under regulatory pressure, with new overnight benchmarks predicted to replace them

Workshop: Curve Calibration

  • Curve calibration
  • Risk management
  • Foreign currency collateral
  • How appearance of risk is changing with the selection of calibration instruments

All curve calibration and collateral examples use production grade open source code (the code is used by banks, CCPs, hedge funds). As the code is open source (Apache 2 license), participants will be able to take away the examples and run them using their own data without limitation.

Day Two

Interest Rate Modelling

  • Modelling with collateral. Dynamic term structure models have been developed to cover collateral discounting. Even if they are partly similar to the single-curve interest rate models, the collateral adds an extra layer of complexity and an extra layer of spreads to deal with. A large part of the financial mathematics and numerical analysis developed in the single-curve framework can be reused, but some additional issues have to be taken into account
  • Modelling vanilla instruments: IRS, OIS, FRA, basis swaps, STIR futures, swaptions, cap/floor, etc.
  • Review of different multi-curve dynamic models proposed in the literature: deterministic spread, full-term structure models, parsimonious model, rational model, additive and multiplicative spreads, and hybrid models
  • Models for multi-currency collateral 
  • Collateral optionality


  • Fall-back clauses are proposed in case of discontinuation of exiting benchmarks. What are those proposals? What is the impact of the proposals on the valuation of existing portfolios? Analysis of vanilla products applying the models developed in the first part of the programme
  • New products associated to new benchmarks, e.g. futures on overnight benchmarks, deliverable swap futures 

Workshop: Multi-curve Stochastic Models

  • Impact of the choice of stochastic model on the price of vanilla instruments 
  • Example of futures and FRA convexity adjustments 
  • Impact of fall-back clauses in case of LIBOR discontinuation

All stochastic model examples also use production grade open source code.

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