The multivariate Black & Scholes market: conditions for completeness and no-arbitrage
Authors:
J. Dhaene, A. Kukush and D. Linders
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
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
Full-text PDF
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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Additional Information
J. Dhaene
Affiliation:
KU Leuven, Leuven, Belgium
Email:
jan.dhaene@kuleuven.be
A. Kukush
Affiliation:
Taras Shevchenko National University, Kyiv, Ukraine
Email:
alexander{\textunderscore}kukush@univ.kiev.ua
D. Linders
Affiliation:
KU Leuven, Leuven, Belgium
Email:
daniel.linders@kuleuven.be
DOI:
https://doi.org/10.1090/S0094-9000-2014-00920-5
Keywords:
Black \& Scholes,
multivariate asset price models,
arbitrage-free,
completeness,
Brownian motion,
risk-neutral probability measure
Received by editor(s):
October 27, 2012
Published electronically:
July 24, 2014
Article copyright:
© Copyright 2014
American Mathematical Society