Incorporating signals into optimal trading
研究了在最优交易框架中纳入马尔可夫信号，证明了最优策略的存在唯一性，并利用欧洲股票逐笔数据验证了订单簿不平衡作为价格预测信号的有效性。
Abstract We incorporate a Markovian signal in the optimal trading framework which was initially proposed by Gatheral et al. (Math. Finance 22:445–474, 2012) and provide results on the existence and uniqueness of an optimal trading strategy. Moreover, we derive an explicit singular optimal strategy for the special case of an Ornstein–Uhlenbeck signal and an exponentially decaying transient market impact. The combination of a mean-reverting signal along with a market impact decay is of special interest, since they affect the short term price variations in opposite directions. Later, we show that in the asymptotic limit where the transient market impact becomes instantaneous, the optimal strategy becomes continuous. This result is compatible with the optimal trading framework which was proposed by Cartea and Jaimungal (Appl. Math. Finance 20:512–547, 2013). In order to support our models, we analyse nine months of tick-by-tick data on 13 European stocks from the NASDAQ OMX exchange. We show that order book imbalance is a predictor of the future price move and has some mean-reverting properties. From this data, we show that market participants, especially high-frequency traders, use this signal in their trading strategies.