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Analytical derivation of the optimal exercise boundary ("free boundary") for the American put option remains an unsolved problem. Even the numerical calculations are challenging and have undesirably long calculation times. We show here comparative evaluation of the immensely helpful "Little Ansatz" that gives the free boundary to high accuracy with negligible calculation time. See Tom Little's The Free Boundary for the American Put Option in the Winter 2020 issue of the Journal of Derivatives.
The red line above is the full, "costly," numerical evaluation of the free boundary. The blue line is the Little Ansatz which consists merely of a few elementary function evaluations.
