Fast Calculation of Prices and Sensitivities of European Options Under Variance Gamma

We present new, fast and accurate methods to calculate the prices and sensitivities of European vanilla and digital options under the Variance Gamma model, and the Variance Gamma PDF. For ATM and near-ATM options with short times to maturity, they are usually much faster than methods based on the (inverse) Fourier transform. We show that interpolation near ATM can be very inaccurate, especially for digitals, whereas the results calculated with our method agree with the benchmarks obtained with the most efficient iFT algorithm