TY - GEN A1 - Ehrhardt, Matthias A1 - Mickens, Ronald E. T1 - Discrete Artificial Boundary Conditions for the Black-Scholes Equation of American Options N2 - In this work we derive an exact discrete artificial boundary condition for the Crank-Nicolson scheme for solving the Black-Scholes equation for the valuation of American options. To ensure stability and to avoid any numerical reflections we derive the artificial boundary condition on a purely discrete level. Since the exact discrete artificial boundary condition includes a convolution with respect to time with a weakly decaying kernel, its numerical evaluation becomes very costly for large-time simulations. As a remedy we construct approximate artificial boundary conditions with a kernel having the form of a finite sum-of-exponentials, which can be evaluated in a very efficient recursion. We prove a simple stability criteria for the approximated artificial boundary conditions. Finally we illustrate the efficiency of the proposed method on several examples and compare it to previously obtained discretized artificial boundary conditions. KW - Black-Scholes equation KW - computational finance KW - option pricing KW - finite difference method KW - artificial boundary condition KW - stability KW - free boundary problem KW - American option Y1 - 2006 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/320 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3200 ER -