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On the pricing and hedging of options for highly volatile periods

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  • Youssef El-Khatib
  • Abdulnasser Hatemi-J

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

  • Youssef El-Khatib & Abdulnasser Hatemi-J, 2013. "On the pricing and hedging of options for highly volatile periods," Papers 1304.4688, arXiv.org.
    • Handle: RePEc:arx:papers:1304.4688
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    References listed on IDEAS

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    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.
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    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.

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    More about this item

    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

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