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Towards a General Theory of Bond Markets

Author

Listed:
  • Björk, Tomas

    (Department of Finance)

  • di Masi, Giovanni

    (Dipartimento di Matematica Pura et Applicata)

  • Kabanov, Yuri

    (Laboratoire de Mathématiques)

  • Runggaldier, Wolfgang

    (Dipartimento di Matematica Pura et Applicata)

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 if an equivalent martingale measure is unique.

Suggested Citation

  • Björk, Tomas & di Masi, Giovanni & Kabanov, Yuri & Runggaldier, Wolfgang, 1996. "Towards a General Theory of Bond Markets," SSE/EFI Working Paper Series in Economics and Finance 143, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0143
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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. 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.
    6. Laurence Carassus & Emmanuel Temam, 2010. "Pricing and Hedging Basis Risk under No Good Deal Assumption," Working Papers hal-00498479, HAL.
    7. 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.
    8. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    9. Marek Rutkowski & Marek Musiela, 1997. "Continuous-time term structure models: Forward measure approach (*)," Finance and Stochastics, Springer, vol. 1(4), pages 261-291.
    10. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
    11. 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 255-271, December.
    12. 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.
    13. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    14. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
    15. 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.

    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:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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