Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation
Fachbereich Mathematik und
Informatik, Johannes Gutenberg-Universität Mainz,
2 UMR-CNRS 5640, Laboratoire MIP, Université Paul Sabatier, Toulouse, France.
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.
Mathematics Subject Classification: 49L25 / 65M06 / 65M12
Key words: High-order compact finite differences / numerical convergence / viscosity solution / financial derivatives.
© EDP Sciences, SMAI, 2004