The multivariate Black & Scholes market: conditions for completeness and no-arbitrage

Dhaene, J.; Kukush, A.; Linders, D.

doi:10.1090/S0094-9000-2014-00920-5

The multivariate Black & Scholes market: conditions for completeness and no-arbitrage

Authors: J. Dhaene, A. Kukush and D. Linders
Journal: Theor. Probability and Math. Statist. 88 (2014), 85-98
MSC (2010): Primary 91B24; Secondary 60H10, 60J60, 60J65
DOI: https://doi.org/10.1090/S0094-9000-2014-00920-5
Published electronically: July 24, 2014
MathSciNet review: 3112636
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Abstract | References | Similar Articles | Additional Information

Abstract:

In order to price multivariate derivatives, there is need for a multivariate stock price model. To keep the simplicity and attractiveness of the one-dimensional Black & Scholes model, one often considers a multivariate model where each individual stock follows a Black & Scholes model, but the underlying Brownian motions might be correlated. Although the classical one-dimensional Black & Scholes model is always arbitrage-free and complete, this statement does not hold true in a multivariate setting.

In this paper, we derive conditions under which the multivariate Black & Scholes model is arbitrage-free and complete.

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