Fractional Skellam processes with applications to finance

By A. Kerss, Nikolai N. Leonenko, Alla Sikorskii. 2014

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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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/12ee7e76ce8bb24ead59b80b562cf9fad9cc8649