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Option pricing during post-crash relaxation times

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  • Dibeh, Ghassan
  • Harmanani, Haidar M.

Abstract

This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices are then estimated using Monte Carlo and finite difference methods. Results of the model show that call option prices after the crash are systematically less than those predicted by the Black–Scholes model. This is a result of the effect of non-constant volatility of the model that causes a volatility skew.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:380:y:2007:i:c:p:357-365
    DOI: 10.1016/j.physa.2007.02.082
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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. Chiarella, Carl & Dieci, Roberto & Gardini, Laura, 2002. "Speculative behaviour and complex asset price dynamics: a global analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 173-197, October.
    3. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 143-151, June.
    4. Dibeh, Ghassan, 2005. "Speculative dynamics in a time-delay model of asset prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 199-208.
    5. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    6. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    7. 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. 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. 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.
    3. 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.
    4. 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.
    5. 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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