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Interest-Rate Modeling with Multiple Yield Curves

Andrea Pallavicini

Banca IMI; Imperial College London - Department of Mathematics

Marco Tarenghi


June 24, 2010

The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe the market of interest rate products. On the other hand, using different yield curves at the same time requires a reformulation of most of the basic assumptions made in interest rate models. In this paper we discuss market evidences that led to the introduction of a series of different yield curves. We then define a HJM framework based on a multi-curve approach, presenting also a bootstrapping algorithm used to fit these different yield curves to market prices of plain-vanilla contracts such as basic Interest Rate Swaps (IRS) and Forward Rate Agreements (FRA). We then show how our approach can be used in practice when pricing other interest rate products, such as forward starting IRS, plain-vanilla European Swaptions, Constant Maturity Swaps (CMS) and CMS spread options, with the final goal to investigate whether the market is actually using a multi-curve approach or not. We finally present some numerical examples for a simple formulation of the framework which embeds by construction the multi-curve structure; once the model is calibrated to market prices of plain-vanilla options, it can be used via a Monte Carlo simulation to price more complicated exotic options.

Number of Pages in PDF File: 27

Keywords: Yield Curve Bootstrap, Yield Curve Interpolation, Discounting Curve, Multi-Curve Framework, Gaussian Models, HJM Framework, Interest Rate Derivatives, Basis Swaps, CMS Swaps, CMS Spread Options, Counterparty Risk, Liquidity Risk

JEL Classification: G13

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Date posted: June 26, 2010  

Suggested Citation

Pallavicini, Andrea and Tarenghi, Marco, Interest-Rate Modeling with Multiple Yield Curves (June 24, 2010). Available at SSRN: https://ssrn.com/abstract=1629688 or http://dx.doi.org/10.2139/ssrn.1629688

Contact Information

Andrea Pallavicini (Contact Author)
Banca IMI ( email )
Largo Mattioli 3
Milan, MI 20121
+39 02 7261 (Phone)
Imperial College London - Department of Mathematics ( email )
South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom
Marco Tarenghi
Mediobanca ( email )
Piazzetta Enrico Cuccia, 1
Milano, MI 20121
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