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Explicit Solutions For A Nonlinear Model Of Financial Derivatives

Author

Listed:
  • L. A. BORDAG

    (Halmstad University, Box 823, 301 18 Halmstad, Sweden)

  • A. Y. CHMAKOVA

    (Fakultät Mathematik, Naturwissenschaften und Informatik, Brandenburgische Technische Universität Cottbus, Universitätsplatz 3/4, 03044 Cottbus, Germany)

Abstract

Families of explicit solutions are found to a nonlinear Black–Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving a nonlinear Black–Scholes equation.

Suggested Citation

  • L. A. Bordag & A. Y. Chmakova, 2007. "Explicit Solutions For A Nonlinear Model Of Financial Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-21.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:01:n:s021902490700407x
    DOI: 10.1142/S021902490700407X
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Maria do Rosário Grossinho & Yaser Faghan Kord & Daniel Sevcovic, 2017. "Pricing Perpetual Put Options by the Black-Scholes Equation with a Nonlinear Volatility Function," Working Papers REM 2017/19, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    4. Maria do Rosario Grossinho & Yaser Faghan Kord & Daniel Sevcovic, 2017. "Analytical and numerical results for American style of perpetual put options through transformation into nonlinear stationary Black-Scholes equations," Papers 1707.00356, arXiv.org.
    5. Maria do Rosário Grossinho & Yaser Kord Faghan & Daniel Ševčovič, 2017. "Pricing Perpetual Put Options by the Black–Scholes Equation with a Nonlinear Volatility Function," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(4), pages 291-308, December.

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