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Pricing European Options under Fractional Black–Scholes Model with a Weak Payoff Function

Author

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  • Farshid Mehrdoust

    (University of Guilan)

  • Ali Reza Najafi

    (University of Guilan)

Abstract

The purpose of this paper is to obtain an explicit solutions of the fractional Black–Scholes model with a weak payoff function. To do this, we derive fractional Black–Scholes equation by creating a self-financing portfolio strategy under Leland’s strategy. Then, we use the Mellin transform method for solving this equation and obtain the price of a European option as a particular case of the proposed solution. A sensitivity analysis is carried out through numerical experiments which shows the differences between Black–Scholes model and the fractional Black–Scholes model. Moreover, an empirical analysis shows that the fractional Black–Scholes model with Hurst exponent greater than one-half is more precise to predict the real market prices than the classical Black–Sholes model.

Suggested Citation

  • Farshid Mehrdoust & Ali Reza Najafi, 2018. "Pricing European Options under Fractional Black–Scholes Model with a Weak Payoff Function," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 685-706, August.
    • Handle: RePEc:kap:compec:v:52:y:2018:i:2:d:10.1007_s10614-017-9715-3
    DOI: 10.1007/s10614-017-9715-3
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    References listed on IDEAS

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    1. Wang, Xiao-Tian & Wu, Min & Zhou, Ze-Min & Jing, Wei-Shu, 2012. "Pricing European option with transaction costs under the fractional long memory stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1469-1480.
    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. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.
    4. 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.
    5. Yuri M. Kabanov & (*), Mher M. Safarian, 1997. "On Leland's strategy of option pricing with transactions costs," Finance and Stochastics, Springer, vol. 1(3), pages 239-250.
    6. Tomas Björk & Henrik Hult, 2005. "A note on Wick products and the fractional Black-Scholes model," Finance and Stochastics, Springer, vol. 9(2), pages 197-209, April.
    7. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    8. Longjin, Lv & Ren, Fu-Yao & Qiu, Wei-Yuan, 2010. "The application of fractional derivatives in stochastic models driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4809-4818.
    9. Stefan Rostek, 2009. "Option Pricing in Fractional Brownian Markets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-00331-8, October.
    10. Salopek, D. M., 1998. "Tolerance to arbitrage," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 217-230, August.
    11. 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.
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    1. Wei-Guo Zhang & Zhe Li & Yong-Jun Liu & Yue Zhang, 2021. "Pricing European Option Under Fuzzy Mixed Fractional Brownian Motion Model with Jumps," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 483-515, August.

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