Incorporating signals into optimal trading

Abstract

Optimal trading is a recent field of research which was initiated by Almgren, Chriss, Bertsimas and Lo in the late 90's. Its main application is slicing large trading orders, in the interest of minimizing trading costs and potential perturbations of price dynamics due to liquidity shocks. The initial optimization frameworks were based on mean-variance minimization for the trading costs. In the past 15 years, finer modelling of price dynamics, more realistic control variables and different cost functionals were developed. The inclusion of signals (i.e. short term predictors of price dynamics) in optimal trading is a recent development and it is also the subject of this work.We incorporate a Markovian signal in the optimal trading framework which was initially proposed by Gatheral, Schied, and Slynko [21] 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 were 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 [10].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 * http://eyaln13.wixsite.com/eyal-neuman arXiv:1704.00847v3 [q-fin.TR] 4 Jun 2018 orderbook imbalance is a predictor of the future price move and it has some mean-reverting properties. From this data we show that market participants, especially high frequency traders, use this signal in their trading strategies.

Mechanics of Good Trade Execution in the Framework of Linear Temporary Market Impact

“…In the case of linear temporary market impact, the paper by Belak and Muhle-Karbe and Ou [BMKO18] is the one in the literature that achieves the greatest generality with respect to the distributional assumptions on the price process S. Indeed, the price process is only assumed to be a totally square integrable special semimartingale. In particular, this weakens the Markovianity assumption in Lehalle and Neumann [LN19], which already generalised the classical setting of Almgren and Chriss [AC00] (price process as arithmetic Brownian motion) and of Gatheral and Schied [GS11] (price process as geometric Brownian motion). The motivation for the increased generality in Belak and Muhle-Karbe and Ou [BMKO18] is provided by the problem of optimal liquidation in target zone models; these are models in which asset prices have reflecting boundaries enforced by regulatory interventions.…”

“…Although the properties of the price trajectory that can be measured do not say much about the distributional properties of the price process, it is the drift of the price process that arguably has the paramount role in the context of liquidation. Recently, the academic literature has worked on incorporating short-term price predictors in the classical framework of optimal trade execution, and this has been done by modelling these price predictors as drifts of the price process (see [LN19]). In particular, the expected trajectory t → E[S t ] influences the trading strategy and it is susceptible to interpretation.…”

“…shortterm price predictors) in the framework of optimal trade execution leads to dynamic optimal strategies (cf. [LN19]). Indeed, signals are incorporated by modelling the price evolution as…”

“…The drift of the price process therefore describes such enforcements and typically disrupt the Markovianity. In Lehalle and Neumann [LN19] instead, the increased generality was motivated by the willingness to incorporate price signals (i.e. short-term price predictors) in the framework of trade execution.…”

“…In the works by Lehalle and Neuman [LN19] and by Belak and Muhle-Karbe and Ou [BMKO18], dynamic solutions to the optimal execution problem with linear temporary market impact are obtained. As explained in the previous paragraph, this is done in particular by relaxing the fuel constraint.…”