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

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Author Info

  • 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)

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    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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 13 (2010)
    Issue (Month): 08 ()
    Pages: 1241-1263

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    Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:08:p:1241-1263

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    Related research

    Keywords: Interest rate modeling; Heath–Jarrow–Morton; Nelson–Siegel; finite-dimensional representation; arbitrage; projection;

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