An Optimal Control Strategy for Execution of Large Stock Orders Using LSTMs
A. Papanicolaou, H. Fu, P. Krishnamurthy, B. Healy, F. Khorrami
备注：
This work was partially supported by 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
本文在Almgren-Chriss模型框架下，结合真实数据与广义幂律，对大额股票订单的执行过程进行仿真。我们研究的具体场景为：在单个交易日内，通过限价订单簿完成大额持仓的平仓操作。由于大额订单会“消耗订单簿深度”——即订单执行会占用最优买/卖价之外的订单簿流动性，因此会产生交易成本。我们采用与交易量成正比的幂律模型刻画订单簿形态，由此推导得出交易成本与交易量的幂次成反比。\n我们将大额订单拆分为一系列小额子订单逐步执行，通过训练长短期记忆（long short term memory, LSTM）神经网络最小化累计交易成本，从而得到近似最优执行策略。我们使用标普100（S&P100）的历史价格与交易量数据，将LSTM策略与基于时间加权平均价格（time-weighted average price, TWAP）和成交量加权平均价格（volume-weighted average price, VWAP）的策略进行对比评估。在执行单只股票的大额订单时，LSTM的输入为全部100只股票的截面数据，包括价格、交易量、TWAP值与VWAP值。通过利用这类截面数据，LSTM能够捕捉不同股票之间交易量与价格波动的相互依赖关系，进而降低当日的交易成本。我们基于S&P100数据的测试结果证实了这一点：LSTM策略的表现始终优于基于TWAP和VWAP的策略。
英文摘要：
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.
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Ecole Polytechnique（巴黎综合理工学院）；Exoduspoint Capital Management（Exoduspoint资本管理公司）
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