Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation

Michel Fournié, Bertram Düring and Ansgar Jüngel

No 04/02, CoFE Discussion Papers from University of Konstanz, Center of Finance and Econometrics (CoFE)

Abstract: A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

Keywords: High-order compact finite differences; numerical convergence; viscosity solution; financial derivatives (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (4)

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