A model of financial market with several interacting assets. Complete market case

Victoria Steblovskaya () and Sergio Albeverio ()
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Victoria Steblovskaya: Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse, 6, D-53115 Bonn, Germany, SFB 256; BiBoS IZKS
Sergio Albeverio: Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse, 6, D-53115 Bonn, Germany, SFB 256; BiBoS IZKS

Finance and Stochastics, 2002, vol. 6, issue 3, 383-396

Abstract: A new model of a financial market is introduced extending the multidimensional Black-Scholes model to the case where several assets can interact with each other even in the absence of noise. Sufficient conditions for the existence of the equivalent martingale measure, absence of arbitrage and completeness are given. In the case of a complete market the pricing of contingent claims based on several assets (e.g. index options) is considered and explicit formulas are derived.

Keywords: Multidimensional Black-Scholes model; linear stochastic differential equations with multiplicative noise; complete market; pricing of contingent claims (search for similar items in EconPapers)
JEL-codes: G10 G12 G13 (search for similar items in EconPapers)
Date: 2002-05-17
Note: received: July 2000; final version received: October 2001
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Citations: View citations in EconPapers (2)

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