IDEAS home Printed from https://ideas.repec.org/a/wsi/ijfexx/v03y2016i01ns2424786316500031.html
   My bibliography  Save this article

Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs

Author

Listed:
  • Foad Shokrollahi

    (Department of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia)

  • Adem Kılıçman

    (Department of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia)

  • Marcin Magdziarz

    (#x2020;Hugo Steinhaus Center, Department of Mathematics, Wrocław University of Technology, Wyspiańskiego 27, 50–370 Wrocław, Poland)

Abstract

This study investigates a new formula for option pricing with transaction costs in a discrete time setting. The value of the financial assets is based on time-changed mixed fractional Brownian motion (MFBM) model. The pricing method is obtained for European call option using the time-changed MFBM model in a discrete time setting. Particularly, the minimal value Cmin(t,St) of an option respect to transaction costs is obtained. Furthermore, the new model for pricing currency option is presented by utilizing the time-changed MFBM model. In addition, the impact of time step Δt, Hurst parameter H and transaction costs α are also investigated, which substantiate that these parameters play a significant role in our pricing formula. Finally, the empirical studies and the simulation findings corroborate the theoretical bases and indicate the time-changed MFBM is a satisfactory model.

Suggested Citation

  • Foad Shokrollahi & Adem Kılıçman & Marcin Magdziarz, 2016. "Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-22, March.
    • Handle: RePEc:wsi:ijfexx:v:03:y:2016:i:01:n:s2424786316500031
    DOI: 10.1142/S2424786316500031
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S2424786316500031
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S2424786316500031?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. 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. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. T. S. Ho & Richard C. Stapleton & Marti G. Subrahmanyam, 1995. "Correlation risk, cross‐market derivative products and portfolio performance," European Financial Management, European Financial Management Association, vol. 1(2), pages 105-124, July.
    4. 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.
    5. Guo, Zhidong & Yuan, Hongjun, 2014. "Pricing European option under the time-changed mixed Brownian-fractional Brownian model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 73-79.
    6. 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.
    7. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    8. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    9. Wei, J.Z. & Duan, J.C., 1999. "Pricing Foreign Currency and Cross-Currency Options Under GARCH," Rotman School of Management - Finance 99-01, Rotman School of Management, University of Toronto.
    10. Piryatinska, A. & Saichev, A.I. & Woyczynski, W.A., 2005. "Models of anomalous diffusion: the subdiffusive case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 375-420.
    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. Ahmadian, D. & Ballestra, L.V. & Shokrollahi, F., 2022. "A Monte-Carlo approach for pricing arithmetic Asian rainbow options under the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. 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.
    3. Ma, Pengcheng & Najafi, Alireza & Gomez-Aguilar, J.F., 2024. "Sub mixed fractional Brownian motion and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Hamidreza Maleki Almani & Foad Shokrollahi & Tommi Sottinen, 2024. "Hedging in Jump Diffusion Model with Transaction Costs," Papers 2408.10785, arXiv.org.
    5. Jeon, Junkee & Kim, Geonwoo, 2022. "Pricing European continuous-installment currency options with mean-reversion," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    6. Dammak, Wael & Hamad, Salah Ben & de Peretti, Christian & Eleuch, Hichem, 2023. "Pricing of European currency options considering the dynamic information costs," Global Finance Journal, Elsevier, vol. 58(C).
    7. Wang, Wensheng, 2019. "Asymptotics for discrete time hedging errors under fractional Black–Scholes models," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 160-170.

    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. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    2. Lv, Longjin & Xiao, Jianbin & Fan, Liangzhong & Ren, Fuyao, 2016. "Correlated continuous time random walk and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 100-107.
    3. Foad Shokrollahi, 2017. "The evaluation of geometric Asian power options under time changed mixed fractional Brownian motion," Papers 1712.05254, arXiv.org.
    4. 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.
    5. Guo, Zhidong & Yuan, Hongjun, 2014. "Pricing European option under the time-changed mixed Brownian-fractional Brownian model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 73-79.
    6. Foad Shokrollahi, 2017. "Fractional delta hedging strategy for pricing currency options with transaction costs," Papers 1702.00037, arXiv.org.
    7. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. Dammak, Wael & Hamad, Salah Ben & de Peretti, Christian & Eleuch, Hichem, 2023. "Pricing of European currency options considering the dynamic information costs," Global Finance Journal, Elsevier, vol. 58(C).
    10. Zghal, Imen & Ben Hamad, Salah & Eleuch, Hichem & Nobanee, Haitham, 2020. "The effect of market sentiment and information asymmetry on option pricing," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    11. Lan-chih Ho & John Cadle & Michael Theobald, 2022. "Portfolio Insurance Strategies," Springer Books, in: Cheng-Few Lee & Alice C. Lee (ed.), Encyclopedia of Finance, edition 0, chapter 62, pages 1437-1465, Springer.
    12. Dupret, Jean-Loup & Hainaut, Donatien, 2022. "A subdiffusive stochastic volatility jump model," LIDAM Discussion Papers ISBA 2022001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Kim, Kyong-Hui & Yun, Sim & Kim, Nam-Ung & Ri, Ju-Hyuang, 2019. "Pricing formula for European currency option and exchange option in a generalized jump mixed fractional Brownian motion with time-varying coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 215-231.
    14. Raymond Chiang & John Okunev & Mark Tippett, 1997. "Stochastic interest rates, transaction costs, and immunizing foreign currency risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(5), pages 579-598, August.
    15. 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.
    16. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 330-344.
    17. Karipova, Gulnur & Magdziarz, Marcin, 2017. "Pricing of basket options in subdiffusive fractional Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 245-253.
    18. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.
    19. Vorst, A. C. F., 1988. "Option Pricing And Stochastic Processes," Econometric Institute Archives 272366, Erasmus University Rotterdam.
    20. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.

    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:ijfexx:v:03:y:2016:i:01:n:s2424786316500031. 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.worldscientific.com/worldscinet/ijfe .

    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.