For models that have an analytically available characteristic function, Fourier inversion is an important computational method for a fast and accurate calculation of plain vanilla option prices. In order to improve the numerical stability of the Fourier inversion, Lord and Kahl  suggested a method to find an optimal contour of integration, taking into account numerical issues such as cancellation and explosion. Rather than having a problem-dependent contour, Joshi and Yang  built on Andersen and Andreasen’s  suggestion, and showed how to use the Black-Scholes formula as a control variate. In this paper we demonstrate that combining both methods can lead to improved accuracy, and that using the optimal contour is highly effective for out-of-the-money and in-the-money options.
Slides presented at the 9th World Congress of the Bachelier Finance Society, in New York, can be found here.