IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i23p4379-4387.html

Subordinated α-stable Ornstein–Uhlenbeck process as a tool for financial data description

Author

Listed:
  • Janczura, Joanna
  • Orzeł, Sebastian
  • Wyłomańska, Agnieszka

Abstract

The classical financial models are based on the standard Brownian diffusion-type processes. However, in the exhibition of some real market data (like interest or exchange rates) we observe characteristic periods of constant values. Moreover, in the case of financial data, the assumption of normality is often unsatisfied. In such cases the popular Vasiček model, that is a mathematical system describing the evolution of interest rates based on the Ornstein–Uhlenbeck process, seems not to be applicable. Therefore, we propose an alternative approach based on a combination of the popular Ornstein–Uhlenbeck process with a stable distribution and subdiffusion systems that demonstrate such characteristic behavior. The probability density function of the proposed process can be described by a Fokker–Planck type equation and therefore it can be examined as an extension of the basic Ornstein–Uhlenbeck model. In this paper, we propose the parameters’ estimation method and calibrate the subordinated Vasiček model to the interest rate data.

Suggested Citation

  • Janczura, Joanna & Orzeł, Sebastian & Wyłomańska, Agnieszka, 2011. "Subordinated α-stable Ornstein–Uhlenbeck process as a tool for financial data description," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4379-4387.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4379-4387
    DOI: 10.1016/j.physa.2011.07.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111005346
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2011.07.007?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. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0501, December.
    3. Krzysztof Burnecki & Joanna Janczura & Rafał Weron, 2011. "Building loss models," Springer Books, in: Pavel Cizek & Wolfgang Karl Härdle & Rafał Weron (ed.), Statistical Tools for Finance and Insurance, chapter 9, pages 293-328, Springer.
    4. Borak, Szymon & Misiorek, Adam & Weron, Rafał, 2010. "Models for heavy-tailed asset returns," SFB 649 Discussion Papers 2010-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    5. repec:hum:wpaper:sfb649dp2010-049 is not listed on IDEAS
    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. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
    2. He, Yue & Kawai, Reiichiro, 2022. "Super- and subdiffusive positions in fractional Klein–Kramers equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    3. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    4. Bielak, Łukasz & Grzesiek, Aleksandra & Janczura, Joanna & Wyłomańska, Agnieszka, 2021. "Market risk factors analysis for an international mining company. Multi-dimensional, heavy-tailed-based modelling," Resources Policy, Elsevier, vol. 74(C).
    5. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    6. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.

    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. Adam Misiorek & Rafal Weron, 2010. "Heavy-tailed distributions in VaR calculations," HSC Research Reports HSC/10/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    2. Burnecki, Krzysztof & Gajda, Janusz & Sikora, Grzegorz, 2011. "Stability and lack of memory of the returns of the Hang Seng index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3136-3146.
    3. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    4. repec:hum:wpaper:sfb649dp2010-061 is not listed on IDEAS
    5. repec:hum:wpaper:sfb649dp2010-059 is not listed on IDEAS
    6. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    7. repec:hum:wpaper:sfb649dp2010-055 is not listed on IDEAS
    8. Magdalena Weglarz & Agnieszka Wylomanska, 2010. "Optimal bidding strategies on the power market based on the stochastic models," HSC Research Reports HSC/10/06, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    9. repec:hum:wpaper:sfb649dp2010-050 is not listed on IDEAS
    10. Rafal Weron, 2005. "Market price of risk implied by Asian-style electricity options," Econometrics 0502003, University Library of Munich, Germany.
    11. Joanna Janczura & Sebastian Orzel & Agnieszka Wylomanska, 2011. "Subordinated alpha-stable Ornstein-Uhlenbeck process as a tool for financial data description," HSC Research Reports HSC/11/03, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    12. Marcin Pitera & Aleksei Chechkin & Agnieszka Wyłomańska, 2022. "Goodness-of-fit test for $$\alpha$$ α -stable distribution based on the quantile conditional variance statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 387-424, June.
    13. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.
    14. repec:hum:wpaper:sfb649dp2010-054 is not listed on IDEAS
    15. Weron, Rafał & Burnecki, Krzysztof, 2004. "Modeling the risk process in the XploRe computing environment," Papers 2004,08, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    16. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    17. Janczura, Joanna & Weron, Rafal, 2010. "An empirical comparison of alternate regime-switching models for electricity spot prices," Energy Economics, Elsevier, vol. 32(5), pages 1059-1073, September.
    18. repec:hum:wpaper:sfb649dp2010-051 is not listed on IDEAS
    19. Jentsch, Carsten & Leucht, Anne & Meyer, Marco & Beering, Carina, 2016. "Empirical characteristic functions-based estimation and distance correlation for locally stationary processes," Working Papers 16-15, University of Mannheim, Department of Economics.
    20. repec:hum:wpaper:sfb649dp2010-056 is not listed on IDEAS
    21. 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.
    22. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0601, December.
    23. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, March.
    24. repec:hum:wpaper:sfb649dp2010-049 is not listed on IDEAS
    25. Makoto Maejima & Gennady Samorodnitsky, 1999. "Certain Probabilistic Aspects of Semistable Laws," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 449-462, September.
    26. Rafał Weron, 2009. "Heavy-tails and regime-switching in electricity prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 457-473, July.
    27. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    28. Furrer, Hansjorg & Michna, Zbigniew & Weron, Aleksander, 1997. "Stable Lévy motion approximation in collective risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 20(2), pages 97-114, September.

    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:phsmap:v:390:y:2011:i:23:p:4379-4387. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.