Fractional Skellam processes with applications to finance

Kerss, Alexander, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Sikorskii, Alla 2014. Fractional Skellam processes with applications to finance. Fractional Calculus and Applied Analysis 17 (2) , pp. 532-551. 10.2478/s13540-014-0184-2

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Abstract

The recent literature on high frequency financial data includes models that use the difference of two Poisson processes, and incorporate a Skellam distribution for forward prices. The exponential distribution of inter-arrival times in these models is not always supported by data. Fractional generalization of Poisson process, or fractional Poisson process, overcomes this limitation and has Mittag-Leffler distribution of inter-arrival times. This paper defines fractional Skellam processes via the time changes in Poisson and Skellam processes by an inverse of a standard stable subordinator. An application to high frequency financial data set is provided to illustrate the advantages of models based on fractional Skellam processes.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	fractional Poisson process; fractional Skellam process; Mittag-Leffler distribution; high frequency financial data
Publisher:	Springer
ISSN:	1311-0454
Last Modified:	25 Oct 2022 09:33
URI:	https://orca.cardiff.ac.uk/id/eprint/59087

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