Optimal placement of a small order in a diffusive limit order book

TL;DR

This paper investigates the optimal placement of limit orders in a diffusive limit order book, revealing how market conditions and time horizons influence order placement strategies and introducing methods to approximate critical parameters.

Contribution

It characterizes the optimal limit order placement policy in a diffusive market and shows how it varies with market drift and time horizon, differing from previous assumptions.

Findings

Existence of a critical time t0 beyond which optimal placement differs from near-best ask.

Optimal placement policy depends on market drift and time horizon.

Proposed a simple approximation method for critical time t0 and order placement.

Abstract

We study the optimal placement problem of a stock trader who wishes to clear his/her inventory by a predetermined time horizon t, by using a limit order or a market order. For a diffusive market, we characterize the optimal limit order placement policy and analyze its behavior under different market conditions. In particular, we show that, in the presence of a negative drift, there exists a critical time t0>0 such that, for any time horizon t>t0, there exists an optimal placement, which, contrary to earlier work, is different from one that is placed "infinitesimally" close to the best ask, such as the best bid and second best bid. We also propose a simple method to approximate the critical time t0 and the optimal order placement.