Abstract.A hybrid algorithm is developed to deal with terminal-boundary value problems for the Black-Scholes equation. The algorithm is semi-analytical in nature. It is based on a combination of the explicit finite difference scheme, which is applied to the time variable, with the Green's function method used to solve the resulting boundary value problems for ordinary deferential equations. Computational potential of this approach is illustrated by computing profiles of solutions for a number of specific problems.

Received: September 14, 2009

AMS Subject Classification: 35C15, 35K20, 35Q80, 35R05, 65M06

Key Words and Phrases: Black-Scholes equation, finite difference, Green's function
method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 2