Limit Order Book Simulation with Generative Adversarial Networks

We propose a nonparametric method for simulating the dynamics of a limit order book using Generative Adversarial Networks (GAN) to learn the conditional distribution of the future state of the order book given its current state from time series of the limit order book. Our method yields a scenario generator for limit order books which captures a range of stylized facts and salient properties of limit order book transitions. We show that the trained generator is also able to correctly reproduce some key properties observed in empirical studies on market impact. In particular, the model exhibits a decaying marginal impact of trade size, higher impact of aggressive orders, as well as a decreasing relation between impact and order book depth