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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
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    References listed on IDEAS

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    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. 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).
    4. Wang, Wensheng, 2019. "Asymptotics for discrete time hedging errors under fractional Black–Scholes models," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 160-170.

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