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Towards a general theory of bond markets (*)

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Author Info

  • 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.

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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 1 (1997)
Issue (Month): 2 ()
Pages: 141-174

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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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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. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, 07.
  2. Laurence Carassus & Emmanuel Temam, 2010. "Pricing and Hedging Basis Risk under No Good Deal Assumption," Working Papers hal-00498479, HAL.
  3. Hinnerich, Mia, 2008. "Inflation-indexed swaps and swaptions," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2293-2306, November.
  4. 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.
  5. Michal Barski & Jerzy Zabczyk, 2010. "Heath-Jarrow-Morton-Musiela equation with linear volatility," Papers 1010.5808, arXiv.org, revised Nov 2010.
  6. 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.
  7. 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.
  8. 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.
  9. 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.

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