Could someone please share a good starting point to learn about Multiple curves? More than exact theorems and proofs, I am mainly interested in reading about -

  1. How to build multiple curves - how to bootstrap simultaneously etc
  2. For a given swap trade, how will my risk look like on these curves.
  3. How should the curves handle different combinations of collateral/netting, forward settle etc.

The closest I got by searching on forums was here, but I'm looking for something more specific.


2 Answers 2


I've always enjoyed OpenGamma's white paper: MULTIPLE CURVE CONSTRUCTION. It's a solid starting point from an implementation perspective.

Andersen & Piterbarg's "Interest Rate Modeling" (Volume 1) also has a good chapter on this topic that's pretty easy to follow.

  • $\begingroup$ Does anyone have a PDF copy of the OpenGamma's white paper: MULTIPLE CURVE CONSTRUCTION? The link above is not valid anymore. Thanks! $\endgroup$
    – Arturo
    Apr 3, 2020 at 5:49

I believe the seminal reference in this matter is:

Masaaki Fujii, Yasufumi Shimada & Akihiko Takahashi (2009). "A note on construction of multiple swap curves with and without collateral". FSA Research Review, Vol. 6, 2010.

I think it gives a good understanding on how to proceed.


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