TY - JOUR

T1 - An optimal control strategy for execution of large stock orders using long short-term memory networks

AU - Papanicolaou, Andrew

AU - Fu, H.

AU - Krishnamurthy, P.

AU - Healy, B.

AU - Khorrami, F.

N1 - Funding Information:
This work was supported in part by National Science Foundation (NSF) grant DMS-1907518 and in part by the New York University Abu Dhabi (NYUAD) Center for Artificial Intelligence and Robotics, funded by Tamkeen under the NYUAD Research Institute Award CG010. We are grateful to the associate editor and anonymous referees, each of whom provided invaluable feedback on this work.
Publisher Copyright:
© 2023 Infopro Digital Risk (IP) Limited.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - long short-term memory (LSTM) networks

KW - optimal execution

KW - order books

KW - price impact

KW - trading volume

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U2 - 10.21314/JCF.2023.003

DO - 10.21314/JCF.2023.003

M3 - Article

AN - SCOPUS:85167344023

SN - 1460-1559

VL - 26

SP - 37

EP - 65

JO - Journal of Computational Finance

JF - Journal of Computational Finance

IS - 4

ER -