Generalized Normal Mean Variance Mixture and Subordinated Brownian Motion
AbstractNormal mean variance mixtures are extensively applied in finance. Under conditions for infinite divisibility they generate subordinated Brownian motions, used to represent stocks returns. The standard generalization to the multivariate setting of normal mean variance mixture does not allow for independence and can incorporate only limited dependence. In this paper we propose a multivariate definition of normal mean variance mixture, named generalized normal mean variance mixture, which includes both independence and high dependence. We give conditions for infinite divisibility and prove that the multivariate Lévy process defined from it is a subordinated Brownian motion. We analyze both the distribution and the related process. In the second part of the paper we use the construction to introduce a multivariate generalized hyperbolic distribution (and process) with generalized hyperbolic margins. We conclude with a numerical example to show the case of calibration and the flexibility of the model in describing dependence.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 42-2007.
Length: 28 pages
Date of creation: Mar 2007
Date of revision:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Elisa Luciano & Patrizia Semeraro, 2007. "Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators," Carlo Alberto Notebooks 42, Collegio Carlo Alberto.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
- Schmidt, Rafael & Hrycej, Tomas & Stutzle, Eric, 2006. "Multivariate distribution models with generalized hyperbolic margins," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 2065-2096, April.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alessandra Calosso).
If references are entirely missing, you can add them using this form.