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A Finite-Dimensional Hjm Model: How Important Is Arbitrage-Free Evolution?

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  • SIOBHÁN DEVIN

    (Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, University College Cork, Ireland)

  • BERNARD HANZON

    (Edgeworth Centre for Financial Mathematics, School of Mathematical Sciences, University College Cork, Ireland)

  • THOMAS RIBARITS

    (European Investment Bank, 98-100, Boulevard Konrad Adenauer, L-2950 Luxembourg, Germany)

Abstract

We consider a two-factor Heath–Jarrow–Morton (HJM) model under the risk neutral measure and show that it may be decoupled into a particular dynamic Nelson–Siegel (NS) model plus a somewhat counter-intuitive adjustment (lying outside the NS family) which keeps it arbitrage-free. We assess the importance of the adjustment for arbitrage-free pricing by comparing the HJM model with a novel NS model which is selected using projection techniques. We analyze forward curves and derivative prices generated by the HJM and projected NS model and consider two real-world case studies. Our analysis shows that the influence of the adjustment term on arbitrage-free evolution is small.

Suggested Citation

  • Siobhán Devin & Bernard Hanzon & Thomas Ribarits, 2010. "A Finite-Dimensional Hjm Model: How Important Is Arbitrage-Free Evolution?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1241-1263.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:08:n:s0219024910006182
    DOI: 10.1142/S0219024910006182
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    References listed on IDEAS

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    1. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2011. "How arbitrage-free is the Nelson-Siegel model?," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 393-407, June.
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    Cited by:

    1. Anastasis Kratsios & Cody Hyndman, 2020. "Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization," Risks, MDPI, vol. 8(2), pages 1-30, April.
    2. Anastasis Kratsios & Cody B. Hyndman, 2017. "Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization," Papers 1710.05114, arXiv.org, revised Dec 2019.

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