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.
Slides presented at the 10th World Congress of the Bachelier Finance Society, in Dublin, can be found here.