SSE/EFI Working Paper Series in Economics and Finance
Towards a General Theory of Bond Markets.
(), Giovanni di Masi, Yuri Kabanov and Wolfgang Runggaldier
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.
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; (follow links to similar papers)
JEL-Codes: G12; G13; (follow links to similar papers)
33 pages, December 1996
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- This paper is published as:
Björk, Tomas, Giovanni di Masi, Yuri Kabanov and Wolfgang Runggaldier, (1997), 'Towards a General Theory of Bond Markets.', Finance and Stochastics, Vol. 1, pages 141-174
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