IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i1d10.1007_s11009-023-09999-w.html
   My bibliography  Save this article

Ornstein - Uhlenbeck Process Driven By $$\alpha$$ α -stable Process and Its Gamma Subordination

Author

Listed:
  • Janusz Gajda

    (University of Warsaw)

  • Aleksandra Grzesiek

    (Hugo Steinhaus Center Wroclaw University of Science and Technology)

  • Agnieszka Wyłomańska

    (Hugo Steinhaus Center Wroclaw University of Science and Technology)

Abstract

The variety and diversity of phenomena surrounding us and easy access to empirical data require either new and more complicated models that allow to capture features to resemble the data. In this paper, we study the Ornstein-Uhlenbeck (OU) process driven by $$\alpha -$$ α - stable Lévy process and delayed by the Gamma subordinator. The considered model captures the important features of the parent process, i.e, the OU process with heavy-tailed-based distribution, however, it also possesses some characteristics that are not adequate to the model without the subordination scenario. Thus, it can be very useful for real data with very specific behavior. The considered model can be considered as the natural extension of the variance Gamma process that arises as the ordinary Brownian motion time changed by the Gamma process. We demonstrate the probabilistic properties of the proposed model and indicate how the theoretical results could be applied for the estimation of the model’s parameters.

Suggested Citation

  • Janusz Gajda & Aleksandra Grzesiek & Agnieszka Wyłomańska, 2023. "Ornstein - Uhlenbeck Process Driven By $$\alpha$$ α -stable Process and Its Gamma Subordination," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09999-w
    DOI: 10.1007/s11009-023-09999-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-09999-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-023-09999-w?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    4. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    5. Janicki, Aleksander & Weron, Aleksander, 1995. "Computer simulation of attractors in stochastic models with α-stable noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 9-19.
    6. Wyłomańska, Agnieszka & Chechkin, Aleksei & Gajda, Janusz & Sokolov, Igor M., 2015. "Codifference as a practical tool to measure interdependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 412-429.
    7. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    8. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    9. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    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. Lu, Ningyun & Huang, Shoujin & Li, Yang & Jiang, Bin & Kaynak, Okyay & Zio, Enrico, 2024. "Dynamic weight-based accelerated test modeling for fault degradation and lifetime analysis," Reliability Engineering and System Safety, Elsevier, vol. 252(C).

    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. Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
    2. Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2019. "Long-term swings and seasonality in energy markets," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1011-1023.
    3. Tiziana Di Matteo & Tomaso Aste, 2002. "How Does The Eurodollar Interest Rate Behave?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 107-122.
    4. repec:uts:finphd:40 is not listed on IDEAS
    5. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September.
    6. Ole E. Barndorff-Nielsen & Neil Shephard, 2012. "Basics of Levy processes," Economics Papers 2012-W06, Economics Group, Nuffield College, University of Oxford.
    7. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    8. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    9. Bouasker, O. & Letifi, N. & Prigent, J.-L., 2016. "Optimal funding and hiring/firing policies with mean reverting demand," Economic Modelling, Elsevier, vol. 58(C), pages 569-579.
    10. Chang, Lung-fu & Hung, Mao-wei, 2009. "Analytical valuation of catastrophe equity options with negative exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 59-69, February.
    11. John Crosby, 2008. "A multi-factor jump-diffusion model for commodities," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 181-200.
    12. Gonzalo Cortazar & Simon Gutierrez & Hector Ortega, 2016. "Empirical Performance of Commodity Pricing Models: When is it Worthwhile to Use a Stochastic Volatility Specification?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(5), pages 457-487, May.
    13. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2, July-Dece.
    14. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 686-701.
    15. Andrianos E. Tsekrekos & Mark B. Shackleton & Rafał Wojakowski, 2012. "Evaluating Natural Resource Investments under Different Model Dynamics: Managerial Insights," European Financial Management, European Financial Management Association, vol. 18(4), pages 543-575, September.
    16. Cortazar, Gonzalo & Eterovic, Francisco, 2010. "Can oil prices help estimate commodity futures prices? The cases of copper and silver," Resources Policy, Elsevier, vol. 35(4), pages 283-291, December.
    17. Thomas Bollinger & Axel Kind, 2015. "Risk Premiums in the Cross-Section of Commodity Convenience Yields," Working Paper Series of the Department of Economics, University of Konstanz 2015-17, Department of Economics, University of Konstanz.
    18. G. Charles-Cadogan, 2012. "Active Portfolio Management, Positive Jensen-Jarrow Alpha, and Zero Sets of CAPM," Papers 1206.4562, arXiv.org.
    19. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    20. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457, Decembrie.
    21. James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.

    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:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09999-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.