IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v537y2020ics037843711931533x.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711931533X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.122690?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Jie-Cao He & Hsing-Hua Chang & Ting-Fu Chen & Shih-Kuei Lin, 2023. "Upside and downside correlated jump risk premia of currency options and expected returns," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-58, December.
    3. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    4. 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).
    5. Panhong Cheng & Zhihong Xu & Zexing Dai, 2023. "Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment," Mathematics and Financial Economics, Springer, volume 17, number 3, June.
    6. Elisa Alòs & Jorge A. León, 2021. "An Intuitive Introduction to Fractional and Rough Volatilities," Mathematics, MDPI, vol. 9(9), pages 1-22, April.
    7. Anwer, Zaheer & Khan, Ashraf & Kabir Hassan, M. & Rashid, Mamunur, 2022. "Does the regional proximity lead to exchange rate spillover?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 81(C).
    8. J. Cuñado & L. Gil-Alana & F. Gracia, 2009. "US stock market volatility persistence: evidence before and after the burst of the IT bubble," Review of Quantitative Finance and Accounting, Springer, vol. 33(3), pages 233-252, October.
    9. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 3-46.
    10. Feng, Zongbao & Wu, Xianguo & Chen, Hongyu & Qin, Yawei & Zhang, Limao & Skibniewski, Miroslaw J., 2022. "An energy performance contracting parameter optimization method based on the response surface method: A case study of a metro in China," Energy, Elsevier, vol. 248(C).
    11. Saphores, J.D. & Khalaf, L. & Pelletier, D., 2000. "On Jumps and ARCH Effects in Natural Resource Prices. An Application to Stumpage Prices from Pacific Northwest National Forests," Papers 00-03, Laval - Recherche en Energie.
    12. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    13. Peng He, 2012. "Option Portfolio Value At Risk Using Monte Carlo Simulation Under A Risk Neutral Stochastic Implied Volatility Model," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 6(5), pages 65-72.
    14. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    15. Erhard Reschenhofer & Manveer K. Mangat, 2021. "Fast computation and practical use of amplitudes at non-Fourier frequencies," Computational Statistics, Springer, vol. 36(3), pages 1755-1773, September.
    16. Wang, Jian & Zhu, Yuanguo & Gu, Yajing & Lu, Ziqiang, 2021. "Solutions of linear uncertain fractional order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    17. Denisa Banulescu-Radu & Christophe Hurlin & Bertrand Candelon & Sébastien Laurent, 2016. "Do We Need High Frequency Data to Forecast Variances?," Annals of Economics and Statistics, GENES, issue 123-124, pages 135-174.
    18. Krämer, Walter & Sibbertsen, Philipp & Kleiber, Christian, 2001. "Long memory vs. structural change in financial time series," Technical Reports 2001,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    19. Leonidas S. Rompolis & Elias Tzavalis, 2017. "Pricing and hedging contingent claims using variance and higher order moment swaps," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 531-550, April.
    20. Barkoulas, John T. & Baum, Christopher F., 1996. "Long-term dependence in stock returns," Economics Letters, Elsevier, vol. 53(3), pages 253-259, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s037843711931533x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.