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High order compact finite difference schemes for a nonlinear Black-Scholes equation

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  • Düring, Bertram
  • Fournié, Michel
  • Jüngel, Ansgar

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. In particular, the compact schemes of Rigal are generalized. 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 e±cient than the considered classical schemes.

Suggested Citation

  • Düring, Bertram & Fournié, Michel & Jüngel, Ansgar, 2001. "High order compact finite difference schemes for a nonlinear Black-Scholes equation," CoFE Discussion Papers 01/07, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0107
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    References listed on IDEAS

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    Cited by:

    1. Wei, Dongming & Erlangga, Yogi Ahmad & Zhumakhanova, Gulzat, 2024. "A finite element approach to the numerical solutions of Leland’s model," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 582-593.
    2. 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).
    3. 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).

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