Stein factors for variance-gamma approximation in the Wasserstein and Kolmogorov distances

We obtain new bounds for the solution of variance-gamma (VG) Stein equation that are correct form approximations in terms Wasserstein and Kolmogorov metrics. These hold all parameters values four parameter VG class. As an application we explicit distance error a six moment theorem approximation double Wiener-Itô integrals.