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Time-changed geometric fractional Brownian motion and option pricing with transaction costs

Author

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  • Gu, Hui
  • Liang, Jin-Rong
  • Zhang, Yun-Xiu

Abstract

This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black–Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:15:p:3971-3977
    DOI: 10.1016/j.physa.2012.03.020
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    References listed on IDEAS

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    Citations

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    Cited by:

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    2. 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).
    3. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 240-248.
    4. El-Khatib, Youssef & Hatemi-J, Abdulnasser, 2013. "On the pricing and hedging of options for highly volatile periods," MPRA Paper 45272, University Library of Munich, Germany.
    5. 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.
    6. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
    7. 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.
    8. 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.
    9. 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).
    10. Guo, Zhidong & Song, Yukun & Zhang, Yunliang, 2013. "Comment on “Time-changed geometric fractional Brownian motion and option pricing with transaction costs” by Hui Gu et al," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2311-2314.
    11. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2019. "Pricing Derivatives In Hermite Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-27, September.
    12. Wang, Han & Wu, Xingyi & Wu, Di & Nie, Xin, 2019. "Will land development time restriction reduce land price? The perspective of American call options," Land Use Policy, Elsevier, vol. 83(C), pages 75-83.
    13. Foad Shokrollahi, 2018. "Pricing European option with the short rate under Subdiffusive fractional Brownian motion regime," Papers 1805.00792, arXiv.org.
    14. 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).
    15. Mariusz Tarnopolski, 2017. "Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach," Papers 1707.03746, arXiv.org, revised Aug 2017.
    16. Foad Shokrollahi, 2017. "The evaluation of geometric Asian power options under time changed mixed fractional Brownian motion," Papers 1712.05254, arXiv.org.
    17. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    18. 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.
    19. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.

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