IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n352021.html

Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion

Author

Listed:
  • Di Pan
  • Shengwu Zhou
  • Yan Zhang
  • Miao Han

Abstract

Geometric‐average Asian option pricing model with monotonous transaction cost rate under fractional Brownian motion was established. The method of partial differential equations was used to solve this model and the analytical expressions of the Asian option value were obtained. The numerical experiments show that Hurst exponent of the fractional Brownian motion and transaction cost rate have a significant impact on the option value.

Suggested Citation

  • Di Pan & Shengwu Zhou & Yan Zhang & Miao Han, 2013. "Asian Option Pricing with Monotonous Transaction Costs under Fractional Brownian Motion," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:352021
    DOI: 10.1155/2013/352021
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/352021
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/352021?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
    ---><---

    References listed on IDEAS

    as
    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    2. Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
    3. Alòs, Elisa & Mazet, Olivier & Nualart, David, 2000. "Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 121-139, March.
    4. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    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. M. Rezaei & A. R. Yazdanian & A. Ashrafi & S. M. Mahmoudi, 2022. "Numerically Pricing Nonlinear Time-Fractional Black–Scholes Equation with Time-Dependent Parameters Under Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 243-280, June.
    2. Yilun Zhang & Zheng Tang & Hexiang Sun & Yufeng Shi, 2026. "Deep g-Pricing for CSI 300 Index Options with Volatility Trajectories and Market Sentiment," Papers 2601.18804, arXiv.org.
    3. Al–Zhour, Zeyad & Barfeie, Mahdiar & Soleymani, Fazlollah & Tohidi, Emran, 2019. "A computational method to price with transaction costs under the nonlinear Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 291-301.
    4. Jose Cruz & Maria Grossinho & Daniel Sevcovic & Cyril Izuchukwu Udeani, 2022. "Linear and Nonlinear Partial Integro-Differential Equations arising from Finance," Papers 2207.11568, arXiv.org.
    5. Wen Li & Song Wang, 2014. "A numerical method for pricing European options with proportional transaction costs," Journal of Global Optimization, Springer, vol. 60(1), pages 59-78, September.
    6. Shengwu Zhou & Wei Li & Yu Wei & Cui Wen, 2012. "A Positivity‐Preserving Numerical Scheme for Nonlinear Option Pricing Models," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Maria do Rosario Grossinho & Yaser Faghan Kord & Daniel Sevcovic, 2017. "Analytical and numerical results for American style of perpetual put options through transformation into nonlinear stationary Black-Scholes equations," Papers 1707.00356, arXiv.org.
    8. Daniel Sevcovic, 2007. "An iterative algorithm for evaluating approximations to the optimal exercise boundary for a nonlinear Black-Scholes equation," Papers 0710.5301, arXiv.org.
    9. Lesmana, Donny Citra & Wang, Song, 2015. "Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costs," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 318-330.
    10. Maxim Bichuch, 2011. "Pricing a Contingent Claim Liability with Transaction Costs Using Asymptotic Analysis for Optimal Investment," Papers 1112.3012, arXiv.org.
    11. Ahmadian, D. & Farkhondeh Rouz, O. & Ivaz, K. & Safdari-Vaighani, A., 2020. "Robust numerical algorithm to the European option with illiquid markets," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    12. Damgaard, Anders, 2003. "Utility based option evaluation with proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 667-700, February.
    13. Daniel Sevcovic & Magdalena Zitnanska, 2016. "Analysis of the nonlinear option pricing model under variable transaction costs," Papers 1603.03874, arXiv.org.
    14. Daniel Sevcovic & Cyril Izuchukwu Udeani, 2021. "Multidimensional linear and nonlinear partial integro-differential equation in Bessel potential spaces with applications in option pricing," Papers 2106.10498, arXiv.org.
    15. C. Atkinson & S. Kazantzaki, 2009. "Double knock-out Asian barrier options which widen or contract as they approach maturity," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 329-340.
    16. Jiatu Cai & Masaaki Fukasawa, 2014. "Asymptotic replication with modified volatility under small transaction costs," Papers 1408.5677, arXiv.org.
    17. Maxim Bichuch, 2014. "Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment," Finance and Stochastics, Springer, vol. 18(3), pages 651-694, July.
    18. Lai, Tze Leung & Lim, Tiong Wee, 2009. "Option hedging theory under transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 33(12), pages 1945-1961, December.
    19. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
    20. Wei, Dongming & Erlangga, Yogi Ahmad & Zhumakhanova, Gulzat, 2024. "A finite element approach to the numerical solutions of Leland’s model," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 582-593.

    More about this item

    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:wly:jnljam:v:2013:y:2013:i:1:n:352021. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.