Determining European Options Values through Crank-Nicolson Method

Abstract

Options are nowadays transacted within a lot of stock exchanges worldwide. The problem of options gets a special importance due to the fact that many of the managerial decisions can be assimilated to options. The paper deals with numerical methods of financial options evaluation. The mathematical model of determining the values of an option of European type is partial differential equation with an initial condition and two boundaries conditions, and for its solving, finite differences methods can be used. Out of these methods, the Crank-Nicolson method is proposed to be used. As Crank-Nicolson method is an implicit one, applying it leads to a linear system of equations, for whose solving the LU algorithm, Gauss method, Jacobi method, Gauss – Seidel method, method of successive over-relaxations are used.

Keywords

• European options
• values of an option
• Crank – Nicolson Method
• LU algorithm
• Gauss method
• Jacobi method
• Gauss – Seidel method
• method of successive over-relaxations