Far Field Boundary Conditions for Black--Scholes Equations

In this paper we consider the partial differential equations approach for valuing European-style options. In order to solve the equations numerically by finite difference or finite element methods it is necessary to introduce an artificial boundary in order to make the computational domain bounded. We derive pointwise bounds for the error caused by various boundary conditions imposed on the artificial boundary. The error estimates can be used to determine a priori a suitable location for the artificial boundary in terms of a given error tolerance.