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The geometry of multi-curve interest rate models

Author

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  • Claudio Fontana
  • Giacomo Lanaro
  • Agatha Murgoci
Abstract
We study the problems of consistency and of the existence of finite-dimensional realizations for multi-curve interest rate models of Heath-Jarrow-Morton type, generalizing the geometric approach developed by T. Bj\"ork and co-authors in the classical single-curve setting. We characterize when a multi-curve interest rate model is consistent with a given parameterized family of forward curves and spreads and when a model can be realized by a finite-dimensional state process. We illustrate the general theory in a number of model classes and examples, providing explicit constructions of finite-dimensional realizations. Based on these theoretical results, we perform the calibration of a three-curve Hull-White model to market data and analyse the stability of the estimated parameters.

Suggested Citation

  • Claudio Fontana & Giacomo Lanaro & Agatha Murgoci, 2024. "The geometry of multi-curve interest rate models," Papers 2401.11619, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2401.11619
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    References listed on IDEAS

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    1. Flavio Angelini & Stefano Herzel, 2005. "Consistent calibration of HJM models to cap implied volatilities," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(11), pages 1093-1120, November.
    2. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    3. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Post-Print hal-03898927, HAL.
    4. 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.
    5. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    6. Tomas Björk & Lars Svensson, 2001. "On the Existence of Finite‐Dimensional Realizations for Nonlinear Forward Rate Models," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 205-243, April.
    7. Gerhart, Christoph & Lütkebohmert, Eva, 2020. "Empirical analysis and forecasting of multiple yield curves," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 59-78.
    8. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Papers 1801.04994, arXiv.org, revised Feb 2018.
    9. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    10. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    11. Tomas BjÃrk & Andrea Gombani, 1999. "Minimal realizations of interest rate models," Finance and Stochastics, Springer, vol. 3(4), pages 413-432.
    12. Andrea Macrina & Obeid Mahomed, 2018. "Consistent Valuation Across Curves Using Pricing Kernels," Risks, MDPI, vol. 6(1), pages 1-39, March.
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