Dealing with heavy tailed-data is an important task in financial and actuarial modelling. More specifically, simulating large sets of heavy-tailed data from a training set may lead to a better estimation of the Value-at-Risk and, more generally, to a better insight on the inner working of financial ecosystems. To this extent, we leverage data generation algorithms and extreme-value theory to understand heavy-tailed financial signals. However, out of the box Generative Models typically produce data distributions with light tails. In this talk, we will discuss findings on the theoretical and practical aspects of the proposed neural network method, which aims at mitigating the limitation of classical GANs by introducing a heavy-tailed latent noise. We prove that this new method creates samples that are heavy-tailed with the desired tail dependence. Also, as for classical GANs, training may be tricky. We will discuss insights from training, including the selection of optimal parameter ranges, on both synthetic and real datasets.