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Hedging in fractional Black–Scholes model with transaction costs

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  • Shokrollahi, Foad
  • Sottinen, Tommi

Abstract

We consider conditional-mean hedging in a fractional Black–Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently discovered explicit conditional law of the fractional Brownian motion.

Suggested Citation

  • Shokrollahi, Foad & Sottinen, Tommi, 2017. "Hedging in fractional Black–Scholes model with transaction costs," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 85-91.
    • Handle: RePEc:eee:stapro:v:130:y:2017:i:c:p:85-91
    DOI: 10.1016/j.spl.2017.07.014
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    References listed on IDEAS

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    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, Xiao-Tian, 2010. "Scaling and long range dependence in option pricing, IV: Pricing European options with transaction costs under the multifractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 789-796.
    3. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    4. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    5. Wang, Xiao-Tian, 2010. "Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 438-444.
    6. repec:dau:papers:123456789/4654 is not listed on IDEAS
    7. Wang, Xiao-Tian & Zhu, En-Hui & Tang, Ming-Ming & Yan, Hai-Gang, 2010. "Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian–fractional Brownian model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 445-451.
    8. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.
    9. Wang, Xiao-Tian & Yan, Hai-Gang & Tang, Ming-Ming & Zhu, En-Hui, 2010. "Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 452-458.
    10. Sottinen, Tommi & Viitasaari, Lauri, 2017. "Prediction law of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 155-166.
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    Citations

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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. Xie, Jiaquan & Wang, Tao & Ren, Zhongkai & Zhang, Jun & Quan, Long, 2019. "Haar wavelet method for approximating the solution of a coupled system of fractional-order integral–differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 80-89.
    3. 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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