An Optimal Control Strategy for Execution of Large Stock Orders Using LSTMs

In this paper, we simulate the execution of a large stock order with real data and general power law in the Almgren and Chriss model. The example that we consider is the liquidation of a large position executed over the course of a single trading day in a limit order book. Transaction costs are incurred because large orders walk the order book, that is, they consume order book liquidity beyond the best bid/ask. We model the order book with a power law that is proportional to trading volume, and thus transaction costs are inversely proportional to a power of trading volume. We obtain a policy approximation by training a long short term memory (LSTM) neural network to minimize transaction costs accumulated when execution is carried out as a sequence of smaller suborders. Using historical S&P100 price and volume data, we evaluate our LSTM strategy relative to strategies based on time-weighted average price (TWAP) and volume-weighted average price (VWAP). For execution of a single stock, the input to the LSTM is the cross section of data on all 100 stocks, including prices, volumes, TWAPs and VWAPs. By using this data cross section, the LSTM should be able to exploit inter-stock co-dependence in volume and price movements, thereby reducing transaction costs for the day. Our tests on S&P100 data demonstrate that in fact this is so, as our LSTM strategy consistently outperforms TWAP and VWAP-based strategies.