  In this paper we apply the innovative Laplace transformation method
introduced by Sheen, Sloan, and Thom\'ee (IMA J. Numer. Anal., 2003) to solve
the Black-Scholes equation. The algorithm is of arbitrary high convergence rate
and naturally parallelizable. It is shown that the method is very efficient for
calculating various options. Existence and uniqueness properties of the Laplace
transformed Black-Scholes equation are analyzed. Also a transparent boundary
condition associated with the Laplace transformation method is proposed.
Several numerical results for various options under various situations confirm
the efficiency, convergence and parallelization property of the proposed
scheme.
