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The purpose of this paper is to construct the early exercise boundary for aclass of nonlinear Black--Scholes equations with a nonlinear volatilitydepending on the option price. We review a method how to transform the probleminto a solution of a time depending nonlinear parabolic equation defined on afixed domain. Results of numerical computation of the early exercise boundaryfor various nonlinear Black--Scholes equations are also presented.

On a numerical approximation scheme for construction of the early exercise boundary for a class of nonlinear Black-Scholes equations