Finance

Uniqueness

Order book

Mathematics

Market microstructure

Financial economics

Operating system

Market impact

Mean reversion

Limit (mathematics)

Pairs trade

Trading strategy

Mathematical analysis

Alternative trading system

Econometrics

Order (exchange)

Financial market

Economics

Tick size

Programming language

High-frequency trading

SIGNAL (programming language)

Computer science

Transient (computer programming)

Algorithmic trading

Mathematical finance

Finance and Stochastics

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.

Incorporating signals into optimal trading