IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v371y2006i2p565-571.html
   My bibliography  Save this article

Black–Scholes’ model and Bollinger bands

Author

Listed:
  • Liu, Wei
  • Huang, Xudong
  • Zheng, Weian

Abstract

Bollinger bands are well-known in stock market as a popular technical analysis tool. We found that Black–Scholes stock price model had this Bollinger bands property also. In this paper, we give the proof of this phenomenon, and give a new distribution of a statistics generated by the Bollinger bands.

Suggested Citation

  • Liu, Wei & Huang, Xudong & Zheng, Weian, 2006. "Black–Scholes’ model and Bollinger bands," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 565-571.
    • Handle: RePEc:eee:phsmap:v:371:y:2006:i:2:p:565-571
    DOI: 10.1016/j.physa.2006.03.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106003712
    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.2006.03.033?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. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    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. Farias Nazário, Rodolfo Toríbio & e Silva, Jéssica Lima & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2017. "A literature review of technical analysis on stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 115-126.
    2. Li, Long & Bao, Si & Chen, Jing-Chao & Jiang, Tao, 2019. "A method to get a more stationary process and its application in finance with high-frequency data of Chinese index futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1405-1417.

    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. William R. Morgan, 2023. "Finance Must Be Defended: Cybernetics, Neoliberalism and Environmental, Social, and Governance (ESG)," Sustainability, MDPI, vol. 15(4), pages 1-21, February.
    2. Filipe Fontanela & Antoine Jacquier & Mugad Oumgari, 2019. "A Quantum algorithm for linear PDEs arising in Finance," Papers 1912.02753, arXiv.org, revised Feb 2021.
    3. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    4. Jun, Doobae & Ku, Hyejin, 2015. "Static hedging of chained-type barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 317-327.
    5. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    6. Paul Ormerod, 2010. "La crisis actual y la culpabilidad de la teoría macroeconómica," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 12(22), pages 111-128, January-J.
    7. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    8. Kearney, Fearghal & Shang, Han Lin & Sheenan, Lisa, 2019. "Implied volatility surface predictability: The case of commodity markets," Journal of Banking & Finance, Elsevier, vol. 108(C).
    9. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    10. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    11. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    12. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    13. Ammann, Manuel & Kind, Axel & Wilde, Christian, 2003. "Are convertible bonds underpriced? An analysis of the French market," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 635-653, April.
    14. Jeremy Leake, 2003. "Credit spreads on sterling corporate bonds and the term structure of UK interest rates," Bank of England working papers 202, Bank of England.
    15. Suleyman Basak & Georgy Chabakauri, 2012. "Dynamic Hedging in Incomplete Markets: A Simple Solution," The Review of Financial Studies, Society for Financial Studies, vol. 25(6), pages 1845-1896.
    16. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Hedging of Derivatives Using Reinforcement Learning," Papers 2103.16409, arXiv.org.
    17. Kuang, Yu Flora & Qin, Bo, 2009. "Performance-vested stock options and interest alignment," The British Accounting Review, Elsevier, vol. 41(1), pages 46-61.
    18. Dubey, Pradeep & Sondermann, Dieter, 2009. "Perfect competition in an oligopoly (including bilateral monopoly)," Games and Economic Behavior, Elsevier, vol. 65(1), pages 124-141, January.
    19. Saphores, J.D. & Khalaf, L. & Pelletier, D., 2000. "On Jumps and ARCH Effects in Natural Resource Prices. An Application to Stumpage Prices from Pacific Northwest National Forests," Papers 00-03, Laval - Recherche en Energie.
    20. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.

    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:371:y:2006:i:2:p:565-571. 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.