Modern Algorithmic Trading ("Algo") allows institutional investors and traders to liquidate or establish big security positions in a fully automated or low-touch manner. Most existing academic or industrial Algos focus on how to "slice" a big parent order into smaller child orders over a given time horizon. Few models rigorously tackle the actual placement of these child orders. Instead, placement is mostly done with a combination of empirical signals and heuristic decision processes. A self-contained, realistic, and fully functional Child Order Placement (COP) model may never exist due to all the inherent complexities, e.g., fragmentation due to multiple venues, dynamics of limit order books, lit vs. dark liquidity, different trading sessions and rules. In this paper, we propose a reductionism COP model that focuses exclusively on the interplay between placing passive limit orders and sniping using aggressive takeout orders. The dynamic programming model assumes the form of a stochastic linear-quadratic regulator (LQR) and allows closed-form solutions under the backward Bellman equations. Explored in detail are model assumptions and general settings, the choice of state and control variables and the cost functions, and the derivation of the closed-form solutions.
[1]
D. Bertsimas,et al.
Optimal control of execution costs
,
1998
.
[2]
Robert Almgren,et al.
Optimal Trading with Stochastic Liquidity and Volatility
,
2012,
SIAM J. Financial Math..
[3]
Tony F. Chan,et al.
Image processing and analysis - variational, PDE, wavelet, and stochastic methods
,
2005
.
[4]
Gur Huberman,et al.
Optimal Liquidity Trading
,
2000
.
[5]
Hybrid IS-VWAP Dynamic Algorithmic Trading via LQR
,
2017
.
[6]
Jackie Jianhong Shen,et al.
A Pre-Trade Algorithmic Trading Model under Given Volume Measures and Generic Price Dynamics (GVM-GPD)
,
2013,
1309.5046.
[7]
Bruno Bouchard,et al.
Optimal Control of Trading Algorithms: A General Impulse Control Approach
,
2011,
SIAM J. Financial Math..
[8]
Alexander Fadeev,et al.
Optimal execution for portfolio transactions
,
2006
.