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In this paper we propose a deep recurrent architecture for the probabilistic modelling of high-frequency market prices, important for the risk management of automated trading systems. Our proposed architecture incorporates probabilistic mixture models into deep recurrent neural networks. The resulting deep mixture models simultaneously address several practical challenges important in the development of automated highfrequency trading strategies that were previously neglected in the literature: 1) probabilistic forecasting of the price movements; 2) single objective prediction of both the direction and size of the price movements. We train our models on high-frequency Bitcoin market data and evaluate them against benchmark models obtained from the literature. We show that our model outperforms the benchmark models in both a metric-based test and in a simulated trading scenario.

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Intra-day price variations in financial markets are driven by the sequence of orders, called the order flow, that is submitted at high frequency by traders. This paper introduces a novel application of the Sequence Generative Adversarial Networks framework to model the order flow, such that random sequences of the order flow can then be generated to simulate the intra-day variation of prices. As a benchmark, a wellknown parametric model from the quantitative finance literature is selected. The models are fitted, and then multiple random paths of the order flow sequences are sampled from each model. Model performances are then evaluated by using the generated sequences to simulate price variations, and we compare the empirical regularities between the price variations produced by the generated and real sequences. The empirical regularities considered include the distribution of the price log-returns, the price volatility, and the heavy-tail of the log-returns distributions. The results show that the order sequences from the generative model are better able to reproduce the statistical behaviour of real price variations than the sequences from the benchmark.