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financial derivatives.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
Bertram Düring, Michel Fournié, Ansgar Jüngel
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 38 / Issue 2 / March 2004

Published online by Cambridge University Press:

15 March 2004, pp. 359-369

Print publication:

March 2004
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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.