The fractional step method is a method of approximation of evolution equations based on decomposition of the operators they contain. In recent years, operator splitting methods have been developed that enable an efficient and stable numerical solution of PDEs. This contribution is concerned with a wavelet based numerical solution of the Black-Scholes equation for pricing European options. We use an operator splitting method to split the arising system of equations into an symmetric part and into an unsymmetric part. Then, we apply the θ–scheme for the time discretization and wavelets for the space discretization. Consequently, the arising system of equations can be efficiently preconditioned using an wavelet based preconditioning. Numerical examples are given.