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Incompleteness of the bond market with L\'evy noise under the physical measure

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  • Micha{l} Barski

Abstract

The problem of completeness of the forward rate based bond market model driven by a L\'evy process under the physical measure is examined. The incompleteness of market in the case when the L\'evy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure is presented and the corresponding integral representation of local martingales is proven.

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  • Micha{l} Barski, 2015. "Incompleteness of the bond market with L\'evy noise under the physical measure," Papers 1512.03963, arXiv.org.
    • Handle: RePEc:arx:papers:1512.03963
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    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    2. Jacek Jakubowski & Jerzy Zabczyk, 2007. "Exponential moments for HJM models with jumps," Finance and Stochastics, Springer, vol. 11(3), pages 429-445, July.
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