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Forward rate models with linear volatilities

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  • Micha{l} Barski
  • Jerzy Zabczyk

Abstract

Existence of solutions to the Heath-Jarrow-Morton equation of the bond market with linear volatility and general L\'evy random factor is studied. Conditions for existence and non-existence of solutions in the class of bounded fields are presented. For the existence of solutions the L\'evy process should necessarily be without the Gaussian part and without negative jumps. If this is the case then necessary and sufficient conditions for the existence are formulated either in terms of the behavior of the L\'evy measure of the noise near the origin or the behavior of the Laplace exponent of the noise at infinity.

Suggested Citation

  • Micha{l} Barski & Jerzy Zabczyk, 2015. "Forward rate models with linear volatilities," Papers 1512.05321, arXiv.org.
    • Handle: RePEc:arx:papers:1512.05321
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    References listed on IDEAS

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    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    2. 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..
    3. Jacek Jakubowski & Jerzy Zabczyk, 2007. "Exponential moments for HJM models with jumps," Finance and Stochastics, Springer, vol. 11(3), pages 429-445, July.
    4. Damir Filipović & Stefan Tappe, 2008. "Existence of Lévy term structure models," Finance and Stochastics, Springer, vol. 12(1), pages 83-115, January.
    5. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
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