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Towards a general theory of bond markets (*)

Author

Listed:
  • Giovanni Di Masi

    (Dipartimento di Matematica Pura et Applicata, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy)

  • Tomas Björk

    (Department of Finance, Stockholm School of Economics, Box 6501, S-113 83 Stockholm, Sweden)

  • Wolfgang Runggaldier

    (Dipartimento di Matematica Pura et Applicata, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy)

  • Yuri Kabanov

    (Central Economics and Mathematics Institute of the Russian Academy of Sciences and Laboratoire de Mathématiques, Université de Franche-Comté, 16 Route de Gray, F-25030 Besançon Cedex, France)

Abstract

The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trading strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete iff an equivalent martingale measure is unique.

Suggested Citation

  • Giovanni Di Masi & Tomas Björk & Wolfgang Runggaldier & Yuri Kabanov, 1997. "Towards a general theory of bond markets (*)," Finance and Stochastics, Springer, vol. 1(2), pages 141-174.
    • Handle: RePEc:spr:finsto:v:1:y:1997:i:2:p:141-174
    Note: received: March 1996; final version received: October 1996 To the memory of our friend and colleague Oliviero Lessi.
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    Citations

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    Cited by:

    1. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
    2. Michal Barski & Jerzy Zabczyk, 2010. "Heath-Jarrow-Morton-Musiela equation with linear volatility," Papers 1010.5808, arXiv.org, revised Nov 2010.
    3. Hinnerich, Mia, 2008. "Inflation-indexed swaps and swaptions," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2293-2306, November.
    4. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    5. L. Steinruecke & R. Zagst & A. Swishchuk, 2015. "The Markov-switching jump diffusion LIBOR market model," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 455-476, March.
    6. Kühn, Christoph & Stroh, Maximilian, 2013. "Continuous time trading of a small investor in a limit order market," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2011-2053.
    7. Laurence Carassus & Emmanuel Temam, 2010. "Pricing and Hedging Basis Risk under No Good Deal Assumption," Working Papers hal-00498479, HAL.
    8. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in Levy term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 951-959.
    9. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    10. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    11. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    12. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
    13. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
    14. Albeverio, Sergio & Lytvynov, Eugene & Mahnig, Andrea, 2004. "A model of the term structure of interest rates based on Lévy fields," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 251-263, December.
    15. Gapeev Pavel V. & Küchler Uwe, 2006. "On Markovian short rates in term structure models driven by jump-diffusion processes," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 1-17, December.

    More about this item

    Keywords

    Bond market; term structure of interest rates; stochastic integral; Banach space-valued integrators; measure-valued portfolio; jump-diffusion model; martingale measure; arbitrage; market completeness.;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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