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Pricing geometric Asian power options under mixed fractional Brownian motion environment

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  • Prakasa Rao, B.L.S.

Abstract

It has been observed that the stock price process can be modeled with driving force as a mixed fractional Brownian motion with Hurst index H>34 whenever long-range dependence is possibly present. We obtain a closed form expression for the price of a geometric Asian option under the mixed fractional Brownian motion environment. We consider also Asian power options when the payoff function is a power function.

Suggested Citation

  • Prakasa Rao, B.L.S., 2016. "Pricing geometric Asian power options under mixed fractional Brownian motion environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 92-99.
    • Handle: RePEc:eee:phsmap:v:446:y:2016:i:c:p:92-99
    DOI: 10.1016/j.physa.2015.11.013
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    References listed on IDEAS

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    1. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xili & Zhang, Xiaoli, 2012. "Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6418-6431.
    2. 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.
    3. Sun, Lin, 2013. "Pricing currency options in the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3441-3458.
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    Cited by:

    1. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    3. Cai, Chunhao & Cheng, Xuwen & Xiao, Weilin & Wu, Xiang, 2019. "Parameter identification for mixed fractional Brownian motions with the drift parameter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    4. Wenhan Li & Cuixiang Li & Lixia Liu & Mengna Wang, 2021. "Foreign Currency Power Option Pricing Based on Esscher Transform," Computational Economics, Springer;Society for Computational Economics, vol. 58(2), pages 535-548, August.
    5. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    6. Jian Pan & Xiangying Zhou, 2017. "Pricing for options in a mixed fractional Hull–White interest rate model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-15, March.
    7. Yang, Zhaoqiang, 2020. "Default probability of American lookback option in a mixed jump-diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    9. 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.
    10. Wang, Lu & Zhang, Rong & Yang, Lin & Su, Yang & Ma, Feng, 2018. "Pricing geometric Asian rainbow options under fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 8-16.
    11. Liu, Zhibin & Huang, Shan, 2021. "Carbon option price forecasting based on modified fractional Brownian motion optimized by GARCH model in carbon emission trading," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    12. Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.
    13. Foad Shokrollahi, 2017. "The evaluation of geometric Asian power options under time changed mixed fractional Brownian motion," Papers 1712.05254, arXiv.org.
    14. 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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