Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T05:02:43.138Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Stochastic processes Stochastic analysis

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: [email protected]
** Postal address: Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus, Denmark. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bardou, O. (2005). Contrôle dynamique des erreurs de simulation et d'estimation de processus de diffusion. Doctoral thesis. Université Nice Sophia Antipolis.Google Scholar
[2]Brigo, D. and Mercurio, F. (2006). Interest Rate Models–Theory and Practice, 2nd edn. Springer, Berlin.Google Scholar
[3]Fissler, T. and Podolskij, M. (2017). Testing the maximal rank of the volatility process for continuous diffusions observed with noise. Bernoulli 23, 3021–3066.Google Scholar
[4]Jacod, J. and Podolskij, M. (2013). A test for the rank of the volatility process: the random perturbation approach. Ann. Statist. 41, 2391–2427.Google Scholar
[5]Jacod, J., Lejay, A. and Talay, D. (2008). Estimation of the Brownian dimension of a continuous Itô process. Bernoulli 14, 469–498.Google Scholar
[6]Sato, K.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press.Google Scholar