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High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation

Author

Listed:
  • Bertram Düring

    (Fachbereich Mathematik und Informatik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany)

  • Michel Fournié

    (UMR-CNRS 5640, Laboratoire MIP, Université Paul Sabatier, Toulouse 3, 31062 Toulouse Cedex, France)

  • Ansgar Jüngel

    (Fachbereich Mathematik und Informatik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany)

Abstract

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

Suggested Citation

  • Bertram Düring & Michel Fournié & Ansgar Jüngel, 2003. "High Order Compact Finite Difference Schemes for a Nonlinear Black-Scholes Equation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 767-789.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:07:n:s0219024903002183
    DOI: 10.1142/S0219024903002183
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    References listed on IDEAS

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    2. Ahmadian, D. & Farkhondeh Rouz, O. & Ivaz, K. & Safdari-Vaighani, A., 2020. "Robust numerical algorithm to the European option with illiquid markets," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    3. Fournié, Michel & Düring, Bertram & Jüngel, Ansgar, 2004. "Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation," CoFE Discussion Papers 04/02, University of Konstanz, Center of Finance and Econometrics (CoFE).

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