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Fractional Skellam processes with applications to finance

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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.

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Authors and Affiliations

  1. Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4 YH, UK

    Alexander Kerss & Nikolai N. Leonenko

  2. Department of Statistics and Probability, Michigan State University, 619 Red Cedar Road, East Lansing, MI, 48824, USA

    Alla Sikorskii

Authors
  1. Alexander Kerss
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  2. Nikolai N. Leonenko
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  3. Alla Sikorskii
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Correspondence to Alexander Kerss.

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Kerss, A., Leonenko, N.N. & Sikorskii, A. Fractional Skellam processes with applications to finance. fcaa 17, 532–551 (2014). https://doi.org/10.2478/s13540-014-0184-2

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  • DOI: https://doi.org/10.2478/s13540-014-0184-2

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