IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v08y2005i03ns0219024905003013.html
   My bibliography  Save this article

Long Memory Stochastic Volatility In Option Pricing

Author

Listed:
  • SERGEI FEDOTOV

    (School of Mathematics, The University of Manchester, M60 1QD, UK)

  • ABBY TAN

    (School of Mathematics, The University of Manchester, M60 1QD, UK)

Abstract

The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black–Scholes equation involving volatility with long-range dependence. We define the stochastic option price as a sum of classical Black–Scholes price and random deviation describing the risk from the random volatility. By using the fact that the option price and random volatility change on different time scales, we derive the asymptotic equation for this deviation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.

Suggested Citation

  • Sergei Fedotov & Abby Tan, 2005. "Long Memory Stochastic Volatility In Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 381-392.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:03:n:s0219024905003013
    DOI: 10.1142/S0219024905003013
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024905003013
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024905003013?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. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    2. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    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. Sergei Fedotov & Stephanos Panayides, 2004. "An Adaptive Method for Valuing an Option on Assets with Uncertainty in Volatility," Papers cond-mat/0410294, arXiv.org, revised Jan 2006.

    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. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    2. Muchnik, Lev & Bunde, Armin & Havlin, Shlomo, 2009. "Long term memory in extreme returns of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4145-4150.
    3. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    4. Lee, Jae Woo & Eun Lee, Kyoung & Arne Rikvold, Per, 2006. "Multifractal behavior of the Korean stock-market index KOSPI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 355-361.
    5. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    6. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    7. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    8. Liviu-Adrian Cotfas, 2012. "A quantum mechanical model for the rate of return," Papers 1211.1938, arXiv.org.
    9. Manley, Bruce & Niquidet, Kurt, 2010. "What is the relevance of option pricing for forest valuation in New Zealand?," Forest Policy and Economics, Elsevier, vol. 12(4), pages 299-307, April.
    10. Slanina, František, 2010. "A contribution to the systematics of stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3230-3239.
    11. Bertram During & Christian Hendricks & James Miles, 2016. "Sparse grid high-order ADI scheme for option pricing in stochastic volatility models," Papers 1611.01379, arXiv.org.
    12. David Vidal-Tomás & Simone Alfarano, 2020. "An agent-based early warning indicator for financial market instability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 49-87, January.
    13. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, October.
    14. Demidov, Denis & Frahm, Klaus M. & Shepelyansky, Dima L., 2020. "What is the central bank of Wikipedia?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    15. Choi, Jaehyung, 2012. "Spontaneous symmetry breaking of arbitrage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3206-3218.
    16. Joachim Kaldasch, 2015. "Dynamic Model of the Price Dispersion of Homogeneous Goods," Papers 1509.01216, arXiv.org.
    17. Wang, Guochao & Zheng, Shenzhou & Wang, Jun, 2019. "Complex and composite entropy fluctuation behaviors of statistical physics interacting financial model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 97-113.
    18. Jung, Woo-Sung & Kwon, Okyu & Wang, Fengzhong & Kaizoji, Taisei & Moon, Hie-Tae & Stanley, H. Eugene, 2008. "Group dynamics of the Japanese market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 537-542.
    19. Arthur Matsuo Yamashita Rios de Sousa & Hideki Takayasu & Misako Takayasu, 2017. "Detection of statistical asymmetries in non-stationary sign time series: Analysis of foreign exchange data," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-18, May.
    20. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.

    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:wsi:ijtafx:v:08:y:2005:i:03:n:s0219024905003013. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.