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Interest-Rate Modeling with Multiple Yield Curves

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  • Andrea Pallavicini
  • Marco Tarenghi

Abstract

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.

Suggested Citation

  • Andrea Pallavicini & Marco Tarenghi, 2010. "Interest-Rate Modeling with Multiple Yield Curves," Papers 1006.4767, arXiv.org.
  • Handle: RePEc:arx:papers:1006.4767
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    File URL: http://arxiv.org/pdf/1006.4767
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    Citations

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    Cited by:

    1. Dilip Madan, 2015. "Asset pricing theory for two price economies," Annals of Finance, Springer, vol. 11(1), pages 1-35, February.
    2. Cousin, Areski & Maatouk, Hassan & Rullière, Didier, 2016. "Kriging of financial term-structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 631-648.
    3. Fanelli, Viviana, 2016. "A defaultable HJM modelling of the Libor rate for pricing Basis Swaps after the credit crunch," European Journal of Operational Research, Elsevier, vol. 249(1), pages 238-244.
    4. N. Moreni & A. Pallavicini, 2014. "Parsimonious HJM modelling for multiple yield curve dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 199-210, February.
    5. Marco, Bianchetti & Mattia, Carlicchi, 2012. "Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR," MPRA Paper 42248, University Library of Munich, Germany.
    6. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    7. Andrea Pallavicini & Damiano Brigo, 2013. "Interest-Rate Modelling in Collateralized Markets: Multiple curves, credit-liquidity effects, CCPs," Papers 1304.1397, arXiv.org.
    8. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    9. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2014. "A general HJM framework for multiple yield curve modeling," Papers 1406.4301, arXiv.org, revised May 2015.
    10. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2016. "A general HJM framework for multiple yield curve modelling," Finance and Stochastics, Springer, vol. 20(2), pages 267-320, April.
    11. Madan, Dilip B., 2014. "Modeling and monitoring risk acceptability in markets: The case of the credit default swap market," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 63-73.
    12. repec:eee:ejores:v:263:y:2017:i:2:p:707-718 is not listed on IDEAS
    13. repec:wsi:jfexxx:v:01:y:2014:i:01:n:s2345768614500019 is not listed on IDEAS
    14. Damiano Brigo & Andrea Pallavicini, 2014. "CCP Cleared or Bilateral CSA Trades with Initial/Variation Margins under credit, funding and wrong-way risks: A Unified Valuation Approach," Papers 1401.3994, arXiv.org.

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