IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i9p2970-2991.html
   My bibliography  Save this article

Lévy driven moving averages and semimartingales

Author

Listed:
  • Basse, Andreas
  • Pedersen, Jan

Abstract

The aim of the present paper is to study the semimartingale property of continuous time moving averages driven by Lévy processes. We provide necessary and sufficient conditions on the kernel for the moving average to be a semimartingale in the natural filtration of the Lévy process, and when this is the case we also provide a useful representation. Assuming that the driving Lévy process is of unbounded variation, we show that the moving average is a semimartingale if and only if the kernel is absolutely continuous with a density satisfying an integrability condition.

Suggested Citation

  • Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
  • Handle: RePEc:eee:spapps:v:119:y:2009:i:9:p:2970-2991
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00061-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cheridito, Patrick, 2004. "Gaussian moving averages, semimartingales and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 47-68, January.
    2. Braverman, Michael & Samorodnitsky, Gennady, 1998. "Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 1-26, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Harms, Philipp & Stefanovits, David, 2019. "Affine representations of fractional processes with applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1185-1228.
    2. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan, 2018. "Equivalent martingale measures for Lévy-driven moving averages and related processes," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2538-2556.
    3. Barndorff-Nielsen, Ole E. & Benth, Fred Espen & Pedersen, Jan & Veraart, Almut E.D., 2014. "On stochastic integration for volatility modulated Lévy-driven Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 812-847.
    4. Andreas Basse, 2009. "Spectral Representation of Gaussian Semimartingales," Journal of Theoretical Probability, Springer, vol. 22(4), pages 811-826, December.
    5. Basse-O’Connor, Andreas & Rosiński, Jan, 2013. "Characterization of the finite variation property for a class of stationary increment infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1871-1890.
    6. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    7. Ole E. Barndorff-Nielsen, 2016. "Assessing Gamma kernels and BSS/LSS processes," CREATES Research Papers 2016-09, Department of Economics and Business Economics, Aarhus University.
    8. Pakkanen, Mikko S. & Sottinen, Tommi & Yazigi, Adil, 2017. "On the conditional small ball property of multivariate Lévy-driven moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 749-782.
    9. Bender, Christian & Knobloch, Robert & Oberacker, Philip, 2015. "A generalised Itō formula for Lévy-driven Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2989-3022.
    10. Christian Bender & Alexander Lindner & Markus Schicks, 2012. "Finite Variation of Fractional Lévy Processes," Journal of Theoretical Probability, Springer, vol. 25(2), pages 594-612, June.
    11. Basse-O'Connor, Andreas & Graversen, Svend-Erik, 2010. "Path and semimartingale properties of chaos processes," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 522-540, April.
    12. Sauri, Orimar, 2020. "On the divergence and vorticity of vector ambit fields," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6184-6225.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Muniandy, Sithi V. & Uning, Rosemary, 2006. "Characterization of exchange rate regimes based on scaling and correlation properties of volatility for ASEAN-5 countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 585-598.
    2. Pakkanen, Mikko S., 2014. "Limit theorems for power variations of ambit fields driven by white noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1942-1973.
    3. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan, 2018. "Equivalent martingale measures for Lévy-driven moving averages and related processes," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2538-2556.
    4. Chr. Framstad, Nils, 2011. "On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes," Memorandum 20/2011, Oslo University, Department of Economics.
    5. Andreas Basse, 2009. "Spectral Representation of Gaussian Semimartingales," Journal of Theoretical Probability, Springer, vol. 22(4), pages 811-826, December.
    6. Sauri, Orimar, 2020. "On the divergence and vorticity of vector ambit fields," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6184-6225.
    7. Andreas Basse-O'Connor & Raphaël Lachièze-Rey & Mark Podolskij, 2015. "Limit theorems for stationary increments Lévy driven moving averages," CREATES Research Papers 2015-56, Department of Economics and Business Economics, Aarhus University.
    8. Dzhaparidze, Kacha & van Zanten, Harry & Zareba, Pawel, 2005. "Representations of fractional Brownian motion using vibrating strings," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1928-1953, December.
    9. John Appleby & Markus Riedle & Catherine Swords, 2013. "Bubbles and crashes in a Black–Scholes model with delay," Finance and Stochastics, Springer, vol. 17(1), pages 1-30, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:119:y:2009:i:9:p:2970-2991. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.