A FINITE-DIMENSIONAL HJM MODEL: HOW IMPORTANT IS ARBITRAGE-FREE EVOLUTION?

Siobhán Devin (), Bernard Hanzon () and Thomas Ribarits ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 08, 1241-1263

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.

Keywords: Interest rate modeling; Heath–Jarrow–Morton; Nelson–Siegel; finite-dimensional representation; arbitrage; projection (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219024910006182

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