  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 high-frequency 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
