Paper:
We propose an approach to generate realistic and high-fidelity stock market data based on generative adversarial networks. We model the order stream as a stochastic process with finite history dependence, and employ a conditional Wasserstein GAN to capture history dependence of orders in a stock market. We test our approach with actual market and synthetic data on a number of different statistics, and find the generated data to be close to real data.

Review:
This paper proposes a Generative Adversarial Network (GAN) methodology to learn the distribution of limit orders that arrive on an equity market. The proposed approach captures the (mostly discrete) structure in the generated orders; modeling is carried out with a conditional Wasserstein-GAN with a recurrent neural networks in both the generator and critic used to capture the time dependency, and convolutional layers to capture other conditioning information. Experiments are provided on both synthetic and real data.
Overall, the paper is well written and easy to follow. The application of WGAN to modeling financial market microstructure is novel and appropriate: microstructure is probably one of the areas of finance where generative models can be trained with ample data, and overfitting risks can therefore be controlled to some extent. In this respect, the paper brings a valuable contribution, both to finance by proposing a direct generative model of a complex process, and to machine learning by showing a useful application of GANs outside of the traditional domains.
My main reservation with the paper is that the experimental results could be more convincing. In particular, results for real data are shown for only two stocks, representing respectively 20k and 230k orders. Although the trained model captures some aspects of the distribution (e.g. inter-arrival times), it misses others, such as important aspects of the (univariate) price distribution, as well as the best bid-ask dynamics. As they stand, the results appear mostly anecdotal, and lack either a breadth or depth of analysis. It would be sensible for the authors to:
1. Compare their models to other limit-order book simulation models proposed in the financial econometrics literature;
2. Characterize the sensitivity of the learned distribution on the architecture hyperparameters.
For these reasons, it appears difficult to recommend acceptance of the paper in its current state.