This thesis explores the Repeated Richardson extrapolation technique when applied to static replication methodologies in the valuation of European-style barrier options under both the constant elasticity of variance (CEV) model and the jump to default extended constant elasticity of variance (JDCEV) model. The Richardson extrapolation is a computational tool used throughout the literature in order to improve the effciency of numerous numerical methods. In this thesis is going to be studied the benefits of its use when applied to static replication methods.