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Towards a General Theory of Bond Markets

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 143.

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Length: 33 pages
Date of creation: Dec 1996
Date of revision:
Publication status: Published in Finance and Stochastics, 1997, pages 141-174.
Handle: RePEc:hhs:hastef:0143

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Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
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Web page: http://www.hhs.se/
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Related research

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;

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Cited by:
  1. 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.
  2. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, 07.
  3. Laurence Carassus & Emmanuel Temam, 2010. "Pricing and Hedging Basis Risk under No Good Deal Assumption," Working Papers hal-00498479, HAL.
  4. Michal Barski & Jerzy Zabczyk, 2010. "Heath-Jarrow-Morton-Musiela equation with linear volatility," Papers 1010.5808, arXiv.org, revised Nov 2010.
  5. Rama Cont, 2005. "Modeling Term Structure Dynamics: An Infinite Dimensional Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 357-380.
  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. 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.
  8. Hinnerich, Mia, 2008. "Inflation-indexed swaps and swaptions," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2293-2306, November.
  9. Johannes Leitner, 2000. "Convergence of Arbitrage-free Discrete Time Markovian Market Models," CoFE Discussion Paper 00-07, Center of Finance and Econometrics, University of Konstanz.

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