APPROXIMATION OF THE FREE BOUNDARY OF
AN AMERICAN CALL OPTION BY FINITE
DIFFERENCES ON PARALLELOGRAMS
Juan C. Aguilar
Instituto Tecnológico Autónomo de México (ITAM)
Departamento de Matemáticas, México, D.F. 01080
Rio Hondo No. 1 Col. Progreso Tizapan
Delegacion Alvaro Obregon, C.P. 01080, MEXICO D.F.
Abstract. In this work we construct a numerical scheme based on finite differences to approximate the free boundary of an American call option. Points of the free boundary are calculated by approximating the solution of the Black-Scholes partial differential equation with finite differences on domains that are parallelograms for each time step. Numerical results are reported.
AMS Subject Classification: 65M06, 65M32, 91G60
Key Words and Phrases: American call option, free boundary, Black-Scholes equation, Crank-Nicolson discretization method, Newton's method, finite differences


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DOI: 10.12732/ijam.v28i6.4

Volume: 28
Issue: 6
Year: 2015