IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i8p2538-2556.html

Equivalent martingale measures for Lévy-driven moving averages and related processes

Author

Listed:
  • Basse-O’Connor, Andreas
  • Nielsen, Mikkel Slot
  • Pedersen, Jan

Abstract

In the present paper we obtain sufficient conditions for the existence of equivalent local martingale measures for Lévy-driven moving averages and other non-Markovian jump processes. The conditions that we obtain are, under mild assumptions, also necessary. For instance, this is the case for moving averages driven by an α-stable Lévy process with α∈(1,2].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:8:p:2538-2556
    DOI: 10.1016/j.spa.2017.09.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441491730251X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.09.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    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. Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
    3. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    4. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
    Full references (including those not matched with items on IDEAS)

    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. Kais Hamza & Fima C. Klebaner & Zinoviy Landsman & Ying-Oon Tan, 2014. "Option Pricing for Symmetric L\'evy Returns with Applications," Papers 1402.1554, arXiv.org.
    2. Michail Anthropelos & Michael Kupper & Antonis Papapantoleon, 2015. "An equilibrium model for spot and forward prices of commodities," Papers 1502.00674, arXiv.org, revised Jan 2017.
    3. Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 125-145.
    4. Andreas Basse, 2009. "Spectral Representation of Gaussian Semimartingales," Journal of Theoretical Probability, Springer, vol. 22(4), pages 811-826, December.
    5. Michail Anthropelos & Michael Kupper & Antonis Papapantoleon, 2018. "An Equilibrium Model for Spot and Forward Prices of Commodities," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 152-180, February.
    6. Xu, Wei & Odening, Martin & Musshoff, Oliver, 2007. "Indifference Pricing of Weather Insurance," 101st Seminar, July 5-6, 2007, Berlin Germany 9267, European Association of Agricultural Economists.
    7. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    8. Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
    9. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2024. "CBI-time-changed Lévy processes for multi-currency modeling," Annals of Operations Research, Springer, vol. 336(1), pages 127-152, May.
    10. 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.
    11. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
    12. Uwe Kuchler & Stefan Tappe, 2019. "Option pricing in bilateral Gamma stock models," Papers 1907.09862, arXiv.org.
    13. A. Fiori Maccioni, 2011. "The risk neutral valuation paradox," Working Paper CRENoS 201112, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    14. Leonel Pérez-Hernández, 2005. "On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market," Department of Economics and Finance Working Papers EC200505, Universidad de Guanajuato, Department of Economics and Finance.
    15. Anastasia Ellanskaya & Lioudmila Vostrikova, 2013. "Utility maximisation and utility indifference price for exponential semi-martingale models with random factor," Papers 1303.1134, arXiv.org.
    16. David Criens, 2016. "Deterministic Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets," Papers 1609.01621, arXiv.org, revised Dec 2017.
    17. 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.
    18. Nacira Agram & Bernt Øksendal & Jan Rems, 2024. "Deep learning for quadratic hedging in incomplete jump market," Digital Finance, Springer, vol. 6(3), pages 463-499, September.
    19. Nelson Christopher Dzupire & Philip Ngare & Leo Odongo, 2019. "Pricing Basket Weather Derivatives on Rainfall and Temperature Processes," IJFS, MDPI, vol. 7(3), pages 1-14, June.
    20. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:128:y:2018:i:8:p:2538-2556. 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.