Learning a functional control for high-frequency finance

Abstract

We use a deep neural network to generate controllers for optimal trading on high-frequency data. For the first time, a neural network learns the mapping between the preferences of the trader, i.e. risk aversion parameters, and the optimal controls. An important challenge in learning this mapping is that, in intra-day trading, trader's actions influence price dynamics in closed loop via the market impact. The exploration–exploitation tradeoff generated by the efficient execution is addressed by tuning the trader's preferences to ensure long enough trajectories are produced during the learning phase. The issue of scarcity of financial data is solved by transfer learning: the neural network is first trained on trajectories generated thanks to a Monte-Carlo scheme, leading to a good initialization before training on historical trajectories. Moreover, to answer to genuine requests of financial regulators on the explainability of machine learning generated controls, we project the obtained ‘blackbox controls’ on the space usually spanned by the closed-form solution of the stylized optimal trading problem, leading to a transparent structure. For more realistic loss functions that have no closed-form solution, we show that the average distance between the generated controls and their explainable version remains small. This opens the door to the acceptance of ML-generated controls by financial regulators.

Keywords:

• Market microstructure
• Optimal execution
• Neural networks
• Quantitative finance
• Stochastic optimization
• Optimal control

JEL Classification:

• C450
• C580
• C610
• G170
• C630

Open Scholarship

This article has earned the Center for Open Science badge for Open Materials. The materials are openly accessible at https://github.com/arula10101/HFT_NN_paper.

Acknowledgments

The authors are extremely grateful for the fruitful discussions with professor René Carmona, who was also very kind to provide the data we used.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The tile size (ts) stands for how many samples of the inventory we combine with each sampled pair. For ts = 3, each pair $(S_0,\{\mathrm{\Delta }{W}_t{\}}_{t=0}^T)$ becomes three samples: $(Q_0^j,S_0,\{\mathrm{\Delta }{W}_t{\}}_{t=0}^T)$, for $j\in \{1,2,3\}$, where j is the tile index. This is useful when using real data, because we can generate more scenarios than we would ordinarily be able to.

2 For the market impact parameters $(\alpha ,\kappa )$, we estimate the same value for all the stocks through a normalization, then we de-normalize the parameters using the seasonality profile of the stock used in the model.

Additional information

Funding

The work of L. Leal and M. Laurière was supported by NSF [grant number DMS-1716673] and ARO [grant number W911NF-17-1-0578].