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Power option pricing under the unstable conditions (Evidence of power option pricing under fractional Heston model in the Iran gold market)

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  • Dastranj, Elham
  • Sahebi Fard, Hossein
  • Abdolbaghi, Abdolmajid
  • Reza Hejazi, S.

Abstract

Instability and excessive volatilities in the various financial and non-financial markets have increased the importance of risk hedging in investments. So in this paper, the hypothetical options pricing have been done based on fractional Heston model in Iran’s gold market. In fact power option pricing has been driven using fast Fourier transformation (FFT), and maximum likelihood method. The study period has been classified to periods of three months and the profit and loss resulting from this option in each period has been calculated using discount rate based on the consumer price index. Findings indicated in most periods of three months, the model’s determination has been done correctly and the estimated price of power option has prevented the creation of arbitrage opportunity and caused a secure position of investment. But in the two periods related to 2018 due to high volatilities, the power option has created an arbitrage opportunity.

Suggested Citation

  • Dastranj, Elham & Sahebi Fard, Hossein & Abdolbaghi, Abdolmajid & Reza Hejazi, S., 2020. "Power option pricing under the unstable conditions (Evidence of power option pricing under fractional Heston model in the Iran gold market)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s037843711931533x
    DOI: 10.1016/j.physa.2019.122690
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    References listed on IDEAS

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    1. Azadeh Naderifard & Elham Dastranj & S. Reza Hejazi, 2018. "Exact solutions for time-fractional Fokker–Planck–Kolmogorov equation of Geometric Brownian motion via Lie point symmetries," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-15, June.
    2. Kim, Kyong-Hui & Yun, Sim & Kim, Nam-Ung & Ri, Ju-Hyuang, 2019. "Pricing formula for European currency option and exchange option in a generalized jump mixed fractional Brownian motion with time-varying coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 215-231.
    3. Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
    4. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    5. Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
    6. Habibi, Noora & Lashkarian, Elham & Dastranj, Elham & Hejazi, S. Reza, 2019. "Lie symmetry analysis, conservation laws and numerical approximations of time-fractional Fokker–Planck equations for special stochastic process in foreign exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 750-766.
    7. 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.
    8. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2017. "Pricing vulnerable options with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 91-103.
    9. 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.
    10. Elham Dastranj & Roghaye Latifi, 2017. "A comparison of option pricing models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-11, June.
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