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On the minimal number of driving Lévy motions in a multivariate price model

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  16 November 2018

Jean Jacod  and
Mark Podolskij
Jean Jacod*
Affiliation:
Université Pierre et Marie Curie
Mark Podolskij*
Affiliation:
Aarhus University
*
* Postal address: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4 Place Jussieu, 75 005 Paris, France. Email address: jean.jacod@gmail.com
** Postal address: Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus, Denmark. Email address: mpodolskij@math.au.dk
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Abstract

In this paper we consider the factor analysis for Lévy-driven multivariate price models with stochastic volatility. Our main aim is to provide conditions on the volatility process under which we can possibly reduce the dimension of the driving Lévy motion. We find that these conditions depend on a particular form of the multivariate Lévy process. In some settings we concentrate on nondegenerate symmetric α-stable Lévy motions.

Keywords

Factor modelLévy processsemimartingale

MSC classification

Primary: 60H05: Stochastic integrals 60G51: Processes with independent increments; L'evy processes
Secondary: 60G18: Self-similar processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 3 , September 2018 , pp. 823 - 833
Copyright
Copyright © Applied Probability Trust 2018 

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References

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