Journal of Computational Finance

An optimal control strategy for execution of large stock orders using long short-term memory networks

Andrew Papanicolaou, Hao Fu, Prasanth Krishnamurthy, Brian Healy and Farshad Khorrami

  • An appropriately trained LSTM network can deliver improved execution of large stock orders in a limit order book.
  • The major advantage of the LSTM approach is that it uses the entire cross section of market data including any inter-stock co-dependence that may be present in volume or price changes.
  • We backtest the execution of block trades using our trained LSTM network, and find an out-of-sample savings of 1-2 basis points per stock per day compared to TWAP and VWAP algorithms for S&P100 stocks from January 2020 - July 2022.
  • This outperformance by the LSTM model is found in simulated order books with both noiseless and noisy power-law parameter in the price impact function.

We simulate the execution of a large stock order with real data and a general power law in the Almgren and Chriss model. The example 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 price). 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 the trading volume. We obtain a policy approximation by training a long short-term memory (LSTM) neural network to minimize the transaction costs accumulated when execution is carried out as a sequence of smaller suborders. Using historical Standard & Poor’s 100 price and volume data, we evaluate our LSTM strategy relative to strategies based on the 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 interstock codependence in volume and price movements, thereby reducing transaction costs for the day. Our tests on Standard & Poor’s 100 data demonstrate that in fact this is so, as our LSTM strategy consistently outperforms TWAP- and VWAP-based strategies.

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