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Pricing American Call Option by the Black-Scholes Equation with a Nonlinear Volatility Function

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Listed:
  • Maria do Rosário Grossinho
  • Yaser Faghan Kord
  • Daniel Sevcovic

Abstract

In this paper we analyze a nonlinear Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We study the generalized Black-Scholes equation by means of transformation of the free boundary problem (variationalinequalities) into the so-called Gamma equation for the new variable H = S@2SV. Moreover, we reformulate our new problem with PSOR method and construct an effective numerical scheme for discretization of the Gamma equation. Finally, we solve numerically our nonlinear complementarity problem applying PSOR method.

Suggested Citation

  • Maria do Rosário Grossinho & Yaser Faghan Kord & Daniel Sevcovic, 2017. "Pricing American Call Option by the Black-Scholes Equation with a Nonlinear Volatility Function," Working Papers REM 2017/18, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    • Handle: RePEc:ise:remwps:wp0182017
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    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_018_2017.pdf
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    References listed on IDEAS

    as
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    4. Maria do Rosario Grossinho & Yaser Kord Faghan & Daniel Sevcovic, 2016. "Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function," Papers 1611.00885, arXiv.org, revised Nov 2017.
    5. Song-Ping Zhu, 2006. "A New Analytical Approximation Formula For The Optimal Exercise Boundary Of American Put Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1141-1177.
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    8. 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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