A Fast Parallel Implicit Method for Solving Black-Scholes Partial Differential Equation

The Option is well known as one of the typical financial derivatives. In order to determine the price of this option, the finite difference method is used, which must be calculated using the Black―Scholes partial differential equation. In this paper, efficient computation is performed for tridiagonal Toeplitz linear equations which is needed when solving Black―Scholes partial differential equation. Let size of discretization with time is n, and size of discretization for property's value is m, we propose a method to find the solution with the required number of parallel steps of 4n log m, and the required number of processors m + log m.