Refined and Enhanced Fast Fourier Transform Techniques, with an Application to the Pricing of Barrier Options

The fast Fourier transform (FFT) technique is now a standard tool for the numerical calculation of prices of derivative securities. Unfortunately, in many important situations, such as the pricing of contingent claims of European type near expiry, and the pricing of barrier options close to the barrier, the standard implementation of this technique leads to serious systematic errors. We propose a new, fast and efficient, variant of the FFT technique, which is free of these problems, and is as easy to implement as the most common version of FFT. As an example, we show how our method leads to a pricing algorithm for down-and-out barrier put options that is the most efficient one to date, both in terms of the speed and in terms of the accuracy of the computations