IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/45272.html
   My bibliography  Save this paper

On the pricing and hedging of options for highly volatile periods

Author

Listed:
  • El-Khatib, Youssef
  • Hatemi-J, Abdulnasser

Abstract

Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the unconditional volatility of the original asset is increasing during a certain period of time. We consider a market suffering from a financial crisis. We provide the solution for the equation of the underlying asset price as well as finding the hedging strategy. In addition, a closed formula of the pricing problem is proved for a particular case. The suggested formulas are expected to make the valuation of options and the underlying hedging strategies during financial crisis more precise.

Suggested Citation

  • El-Khatib, Youssef & Hatemi-J, Abdulnasser, 2013. "On the pricing and hedging of options for highly volatile periods," MPRA Paper 45272, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:45272
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/45272/1/MPRA_paper_45272.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Savit, R., 1989. "Nonlinearities And Chaotic Effects In Options Prices," Papers 184, Columbia - Center for Futures Markets.
    2. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
    3. Dibeh, Ghassan & Harmanani, Haidar M., 2007. "Option pricing during post-crash relaxation times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 357-365.
    4. Fabrizio Lillo & Rosario N. Mantegna, 2001. "Power law relaxation in a complex system: Omori law after a financial market crash," Papers cond-mat/0111257, arXiv.org, revised Jun 2003.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Youssef El-Khatib & Abdulnasser Hatemi-J, 2017. "Computation of second order price sensitivities in depressed markets," Papers 1705.02473, arXiv.org, revised Jan 2018.

    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. El-Khatib Youssef, 2014. "A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 1-6, November.
    2. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    3. Lv, Longjin & Xiao, Jianbin & Fan, Liangzhong & Ren, Fuyao, 2016. "Correlated continuous time random walk and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 100-107.
    4. Guo, Zhidong & Yuan, Hongjun, 2014. "Pricing European option under the time-changed mixed Brownian-fractional Brownian model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 73-79.
    5. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2019. "Pricing Derivatives In Hermite Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-27, September.
    6. Youssef El-Khatib & Abdulnasser Hatemi-J, 2023. "On a regime switching illiquid high volatile prediction model for cryptocurrencies," Journal of Economic Studies, Emerald Group Publishing Limited, vol. 51(2), pages 485-498, July.
    7. Zghal, Imen & Ben Hamad, Salah & Eleuch, Hichem & Nobanee, Haitham, 2020. "The effect of market sentiment and information asymmetry on option pricing," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    8. Dibeh, Ghassan & Harmanani, Haidar M., 2007. "Option pricing during post-crash relaxation times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 357-365.
    9. Mariusz Tarnopolski, 2017. "Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach," Papers 1707.03746, arXiv.org, revised Aug 2017.
    10. Paul Brockman & Mustafa Chowdhury, 1997. "Deterministic versus stochastic volatility: implications for option pricing models," Applied Financial Economics, Taylor & Francis Journals, vol. 7(5), pages 499-505.
    11. Youssef El-Khatib & Abdulnasser Hatemi-J, 2017. "Computation of second order price sensitivities in depressed markets," Papers 1705.02473, arXiv.org, revised Jan 2018.
    12. M. Rezaei & A. R. Yazdanian & A. Ashrafi & S. M. Mahmoudi, 2022. "Numerically Pricing Nonlinear Time-Fractional Black–Scholes Equation with Time-Dependent Parameters Under Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 243-280, June.
    13. Gong, Pu & Dai, Jun, 2017. "Pricing real estate index options under stochastic interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 309-323.
    14. Foad Shokrollahi, 2017. "The evaluation of geometric Asian power options under time changed mixed fractional Brownian motion," Papers 1712.05254, arXiv.org.
    15. Foad Shokrollahi & Adem Kılıçman & Marcin Magdziarz, 2016. "Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-22, March.
    16. Foad Shokrollahi, 2018. "Pricing European option with the short rate under Subdiffusive fractional Brownian motion regime," Papers 1805.00792, arXiv.org.
    17. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.
    18. Ben Abdallah, Skander & Lasserre, Pierre, 2016. "Asset retirement with infinitely repeated alternative replacements: Harvest age and species choice in forestry," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 144-164.
    19. Kau, James B. & Keenan, Donald C., 1999. "Patterns of rational default," Regional Science and Urban Economics, Elsevier, vol. 29(6), pages 765-785, November.
    20. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.

    More about this item

    Keywords

    Asset Pricing and Hedging; Options; Financial Crisis; Black and Scholes formula.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G01 - Financial Economics - - General - - - Financial Crises
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:45272. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.