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The aim of this paper is to solve a free boundary problem arising in pricing Americanput options.It is known that the free boundary (optimal exercise boundary) satises a "nonstandard" Volterra integral equation.This Volterra integral equation is resolved by a high-order collocation method based on graded meshes.Then the value of Americanput option is obtained by solving a Black-Scholes equation in the semi-interval with the computed free boundary and the infinite boundary by a moving mesh method.A feasible time-dependent artificial boundary is constructed to fulfil the solution process.Numerical examples are provided to show the efficiency of the approach.