Incorporating order-flow into optimal execution

Abstract

We provide an explicit closed-form strategy for an investor who executes a large order when market order-flow from all agents, including the investor's own trades, has a permanent price impact. The strategy is found in closed-form when the permanent and temporary price impacts are linear in the market's and investor's rates of trading. We do this under very general assumptions about the stochastic process followed by the order-flow of the market. The optimal strategy consists of an Almgren-Chriss execution strategy adjusted by a weightedaverage of the future expected net order-flow (given by the difference of the market's rate of buy and sell market orders) over the execution trading horizon and proportional to the ratio of permanent to temporary linear impacts. We use historical data to calibrate the model to Nasdaq traded stocks and use simulations to show how the strategy performs.

Mean-Field Games and Ambiguity Aversion

“…which is the same as the equations found in Cartea and Jaimungal (2016) -where the authors study the effect of order-flow in an optimal execution problem for a single agent.…”

“…Section 2.3 describes the player dynamics, with the addition of noise traders as in Cartea and Jaimungal (2016), as well as HFTs as minor agents. This setting incorporates permanent price impact from all traders and accounts for the interaction between the major and minor agents.…”

“…The reader is referred to Jaimungal and Kinzebulatov (2014) and Cartea and Jaimungal (2016) for an illustration of how the parameter a 0 may be estimated from market data for the case of a single agent. The cash process dynamics of the major agent is given by…”

“…In the top figure, the absolute inventory level is plotted, while the second figure describes the difference in inventory when the broker uses the MFG strategy and when they ignore the presence of HFT traders. In comparison to Cartea and Jaimungal (2016), the trading speed of the major agent initially speeds up at the start and end of the liquidation period in order to take advantage of the relatively higher stock price, and slows down in the middle to minimize the amount of stocks sold when the mid-price is at its lowest point. Additionally, we can see that while the mean-field execution strategy starts off with a lower average execution price, it makes up for this setback later on when the minor agent needs to buy back stock.…”

“…In optimal execution problems, an agent is required to choose an efficient trading strategy for liquidating/acquiring a portfolio containing a large quantity of a given security in order to maximize her expected wealth (by minimizing cost or maximizing profit). In this problem formulation, there is a tradeoff between trading slowly to reduce market impact, or execution cost, and trading fast to reduce the risk of future uncertainty in prices (see e.g., Almgren and Chriss (2001); ; Gatheral et al (2012); Guéant and Lehalle (2013);Jaimungal and Kinzebulatov (2014); Cartea and Jaimungal (2016) among many others). Optimal limit order placement aims instead to benefit from buying low and selling high and benefit from the bid-ask spread without being adversely selected.…”