# American Institute of Mathematical Sciences

July  2016, 21(5): 1435-1444. doi: 10.3934/dcdsb.2016004

## Convergence rate of free boundary of numerical scheme for American option

 1 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260 2 Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556 3 Department of Mathematics, Tongji University, Shanghai 200092 4 School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006

Received  September 2013 Published  April 2016

Based on the optimal estimate of convergence rate $O(\Delta x)$ of the value function of an explicit finite difference scheme for the American put option problem in [6], an $O(\sqrt{\Delta x})$ rate of convergence of the free boundary resulting from a general compatible numerical scheme to the true free boundary is proven. A new criterion for the compatibility of a generic numerical scheme to the PDE problem is presented. A numerical example is also included.
Citation: Xinfu Chen, Bei Hu, Jin Liang, Yajing Zhang. Convergence rate of free boundary of numerical scheme for American option. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1435-1444. doi: 10.3934/dcdsb.2016004
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