European Options Evaluation Through Numerical Method

The present paper is meant to describe the finite differences methods necessary to determine the value of financial options. In addition is presented the mathematic model of rating European type options. Value determination of an option is made through solving an equation with derivatives. Finding the analytical solutions is not at hand, reason for which the problem of determining numerical solutions is raised. Next, reference is made to the approximations of model in cause and three methods are intended to be solved: an explicit method, Hyman-Kaplan method and Crank-Nicolson method. As Hyman-Kaplan method is an implicit method, a linear system of equations is obtained whose solution is to be found in LU algorithm. It is also the case of the Crank-Nicolson method whose system of equations finds its solution in Gauss method, Jacobi method, Gauss-Seidel method and the method of successive overrelaxations. Finally, other finite differences methods are reviewed in order to solve the diffusion equation