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On the control of the difference between two Brownian motions: a dynamic copula approach

On the control of the difference between two Brownian motions: a dynamic copula approach AbstractWe propose new copulae to model the dependence between two Brownian motions and to controlthe distribution of their difference. Our approach is based on the copula between the Brownian motion andits reflection. We show that the class of admissible copulae for the Brownian motions are not limited to theclass of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survivalfunction of the difference between two Brownian motions to have higher value in the right tail than in theGaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range ofpossible values for is the same for Markovian pairs and all pairs of Brownianmotions, that is with φ being the cumulative distribution function of a standard Gaussianrandom variable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

On the control of the difference between two Brownian motions: a dynamic copula approach

Deschatre, Thomas
Dependence Modeling , Volume 4 (1): 1 – Jul 28, 2016
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Publisher
de Gruyter
Copyright
© 2016 Thomas Deschatre
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2016-0007
Publisher site
See Article on Publisher Site

Abstract

AbstractWe propose new copulae to model the dependence between two Brownian motions and to controlthe distribution of their difference. Our approach is based on the copula between the Brownian motion andits reflection. We show that the class of admissible copulae for the Brownian motions are not limited to theclass of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survivalfunction of the difference between two Brownian motions to have higher value in the right tail than in theGaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range ofpossible values for is the same for Markovian pairs and all pairs of Brownianmotions, that is with φ being the cumulative distribution function of a standard Gaussianrandom variable.

Journal

Dependence Modeling – de Gruyter

Published: Jul 28, 2016

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