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Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs. (English) Zbl 1175.91071
Summary: This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of the numerical approximation of the Gamma of the option, previously obtained. Results are illustrated with numerical examples.
91B25Asset pricing models
91G20Derivative securities
35K55Nonlinear parabolic equations
65M12Stability and convergence of numerical methods (IVP of PDE)
39A10Additive difference equations