An efficient application of the repeated Richardson extrapolation technique to option pricing

In financial engineering one has frequently to deal with approximate results that are obtained by iterative methods or computational procedures depending on some parameter (e.g. the time-step). Often the convergence of numerical schemes is slow and this may be a serious problem to their use in practice. For this reason, acceleration techniques, such as Richardson extrapolation, have been studied and applied. In this contribution, we implement an efficient numerical method based on repeated Richardson extrapolation for the valuation of American options, paying particular attention to the choice of both the sequence of stepsizes and the order. In particular, we apply the method to the randomization approach proposed by Carr (1998), thus improving its accuracy by choosing a convenient sequence of stepsizes.