Repeated Spatial Extrapolation: An Extraordinarily Efficient Approach for Option Pricing

Abstract

A numerical approach for option pricing is proposed which is based on the use of the repeated Richarsdon extrapolation procedure along the price variable. Such a technique, which is applied in conjunction with the classical (centered) three-point finite difference scheme, is tested on two benchmark test-cases, namely the pricing of a European vanilla Call option and the pricing of a European digital Call option under the Black-Scholes model. Even if the final solutions of these problems are non-smooth, the novel extrapolation approach turns out to be extraordinarily efficient. In particular, the option prices can be computed with errors of order 10e-12 or 10e-13 in only some hundredths of second. To the best of our knowledge, these levels of performance are much higher than those that can be achieved using the lattice-based option pricing methods that have been proposed so far.