Title: An Euler-based GAN for time series. Abstract: A new model of generative adversarial networks for time series based on Euler scheme and Wasserstein distances including Sinkhorn divergence is proposed. Euler scheme improves stability of learning, provides meaningful learning parameters such as drift and volatility while allowing the representation of a large class of processes. We test our Euler GAN generations with usual Monte Carlo simulations in one-dimension and in a multi-dimensional case. We show how the proposed methodology can be combined with transfer learning to include the latest historical dataset features. The approach is tested on financial indicators computation on S\&P500 and on an option hedging problem. 