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Towards a General Theory of Bond Markets

  • 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)

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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Paper provided by Stockholm School of Economics in its series SSE/EFI 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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