Repeated spatial extrapolation: An extraordinarily efficient approach for option pricing

• The repeated spatial extrapolation yields extraordinarily efficient approximations of European vanilla and digital option prices.
• The repeated spatial extrapolation has not been used so far for option pricing.
• We show that the repeated spatial extrapolation achieves superior accuracy even if the final solutions are discontinuous.
• The repeated spatial extrapolation neatly outperforms the already existing finite difference approaches.

Various finite difference methods for option pricing have been proposed. In this paper we demonstrate 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 under the Black–Scholes model, and show that, if the payoff functions are dealt with properly, then errors close to the machine precision are obtained in only some hundredths of a second.