Duality between matrix variate t and matrix variate V.G. distributions
The (univariate) t-distribution and symmetric V.G. distribution are competing models [D.S. Madan, E. Seneta, The variance gamma (V.G.) model for share market returns, J. Business 63 (1990) 511-524; T.W. Epps, Pricing Derivative Securities, World Scientific, Singapore, 2000 (Section 9.4)] for the distribution of log-increments of the price of a financial asset. Both result from scale-mixing of the normal distribution. The analogous matrix variate distributions and their characteristic functions are derived in the sequel and are dual to each other in the sense of a simple Duality Theorem. This theorem can thus be used to yield the derivation of the characteristic function of the t-distribution and is the essence of the idea used by Dreier and Kotz [A note on the characteristic function of the t-distribution, Statist. Probab. Lett. 57 (2002) 221-224]. The present paper generalizes the univariate ideas in Section 6 of Seneta [Fitting the variance-gamma (VG) model to financial data, stochastic methods and their applications, Papers in Honour of Chris Heyde, Applied Probability Trust, Sheffield, J. Appl. Probab. (Special Volume) 41A (2004) 177-187] to the general matrix generalized inverse gaussian (MGIG) distribution.
Volume (Year): 97 (2006)
Issue (Month): 6 (July)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
- Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
- Dreier, I. & Kotz, S., 2002. "A note on the characteristic function of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 221-224, April.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1467-1475. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.