Abstract

The aim of this paper is to solve a free boundary problem arising in pricing American put options. It is known that the free boundary (optimal exercise boundary) satisfies a “nonstandard” Volterra integral equation. This Volterra integral equation is resolved by a high-order collocation method based on graded meshes. With the computed free boundary, a Black-Scholes equation for pricing the American put options is solved by a moving mesh method. Numerical examples are provided to confirm the efficiency of the approach.

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