Optimal Placement in a Limit Order Book

Abstract

Please scroll down for article-it is on subsequent pagesINFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org Abstract Algorithmic trading refers to the automatic and rapid trading of large quantities with orders specified and implemented by an algorithm. Roughly speaking, algorithmic trading is based on two different time scales: the daily or weekly scale and a smaller (10-to 100-second) time scale. These two time scales essentially reflect the two steps by which the traders slice and place orders. The first step is to optimally slice big orders into smaller ones on a daily basis with the goal to minimize the price impact and/or to maximize the expected utility; the second step is to optimally place the orders within seconds. The former is the well-known optimal execution problem, and the latter is the much less studied optimal placement problem. This paper reviews several simple models and approaches for the optimal placement problem. Several most relevant statistical issues are presented, together with a brief discussion on the key differences between the system of limit order book and the multiclass queues with reneging.

Multivariate Transient Price Impact and Matrix-Valued Positive Definite Functions

“…A more comprehensive list of references can be found in Gatheral and Schied [2013]. We also refer to Guo [2013] for an introduction to the microscopic order book picture that is behind the mesoscopic models mentioned above.…”

Optimal trading with alpha predictors

“…We have shown how the optimal strategy can be expressed in terms of the objective function, which is defined by the HJB equation (22). An exact analytical solution of this equation seems out of reach, therefore for practical purposes, we propose using the solution that comes from ignoring the source term −Ku 2 in (22), that is:…”

“…that is we write V as an expansion in 1/K. Plugging the ansatz (83) in the HJB equation (22) and collecting terms of the same order in 1/K, we can write down an equation for any term in the expansion (83), and solve the equation (22) iteratively. We describe this prescription in details for the first two terms V 0 and V 1 .…”

“…Another rather separated stream of literature has studied the use of limit orders both for the liquidation [14,15] and market-making [16]- [20]. The problem of optimally placing market versus limit orders under the possibility of partial execution was studied in [21,22,23]. For market-making, the main problem is the optimal price of the limit orders and the inventory risk.…”

Dynamics of Order Positions and Related Queues in a Limit Order Book

“…As a result, one of the most rapidly growing research areas in financial mathematics has been centered around modeling LOB dynamics and/or minimizing the inventory/execution risk with consideration of the microstructure of LOB. A few examples include [3,4,6,7,17,18,22,21,26,27,28,38,41,42,45,47,50].…”