COMPLETENESS OF BOND MARKET DRIVEN BY LÉVY PROCESS

Michał Barski () and Jerzy Zabczyk ()
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Michał Barski: Mathematics Department, Cardinal Stefan Wyszyński University in Warsaw, Warsaw, Poland
Jerzy Zabczyk: Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 05, 635-656

Abstract: The completeness problem of the bond market model with the random factors determined by a Wiener process and Poisson random measure is studied. Hedging portfolios use bonds with maturities in a countable, dense subset of a finite time interval. It is shown that under natural assumptions the market is not complete unless the support of the Lévy measure consists of a finite number of points. Explicit constructions of contingent claims which cannot be replicated are provided.

Keywords: Bond market; completeness; Lévy term structure (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219024910005942

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