Abstract
We are focused with the numerical approximation of the popular Black-Scholes model for derivative pricing. To this aim, several finite difference methods have been proposed. In this talk, we show how a very simple approach, namely the repeated spatial extrapolation, can perform extremely better than the finite difference schemes that have been developed so far. In particular, we consider the problem of pricing vanilla and digital options, and show how to obtain errors close to the machine precision in only some hundredths of a second. Some extensions of the proposed numerical approach to barrier options and to jump-diffusion models will be discussed.
