Optimal Portfolio Liquidation with Limit Orders

Abstract

This paper addresses portfolio liquidation using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidity-consuming orders like Obizhaeva and Wang in [35], we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portfolio. Most practitioners address these two issues separately: they compute an optimal trading curve and they then send orders to the markets to try to follow it. The results obtained in this paper can be interpreted and used in two ways: (i) we solve simultaneously the two problems and provide a strategy to liquidate a portfolio over a few hours, (ii) we provide a tactic to follow a trading curve over slices of a few minutes. As far as the model is concerned, the interactions of limit orders with the market are modeled via a point process pegged to a diffusive "fair price". A Hamilton-Jacobi-Bellman equation is used to solve the control problem involving both non-execution risk and price risk. Backtests are carried out to exemplify the use of our results, both on long periods of time (for the entire liquidation process) and on slices of 5 minutes (to follow a given trading curve).

Optimal Placement in a Limit Order Book

“…The idea then is to maximize the profit by playing with the spread between the bid and ask prices, while controlling the inventory risk and the execution risk. See for example, Avelaneda and Stoikov (2008) [8], Bayraktar and Ludkovski (2012) [9], Cartea and Jaimungal (2013) [14], Cartea, Jaimugal, and Ricci (2011) [15], Veraarta (2010) [49], Guilbaud and Pham (2011) [29], Guéant, Lehalla, and Tapia (2012) [28], and Horst, Lehalle and Li (2013) [33]. There are also order scheduling problems especially when orders can be placed in different exchanges with different fee structures.…”

Market Making and Portfolio Liquidation Under Uncertainty

“…On the other hand, the presence of market risk favors faster trading. An optimal schedule of a large order may involve the use of market orders and limit orders in combination, as well as a routing of the orders to different exchanges including dark-pools [13,19,28,29,32,34,46,47]. During the continuous auction process implemented by most electronic trading pools, market participants send their orders to a queuing system where a first-in-first-out queue stands at each possible price.…”

“…While a few papers attempt to consider the problem at the level of the interactions with the order book [2,53,55], most of them focus on the dynamics initiated by aggressive orders hitting a resilient order book and ignore trading with passive orders. In fact, optimal liquidation with limit orders included has only been studied very recently [10,19,32,34]. In this paper we consider trading algorithms which are at the most passive end of the spectrum and we focus on algorithms which use only passive limit orders placed in the limit order book.…”

Optimal Placement in a Limit Order Book

“…The profit is a reward for the market maker for his or her service to provide the liquidity to the market. For instance, Avellaneda and Stoikov [7], Bayraktar and Ludkovski [8], Cartea and Tutorials in Operations Research, c 2013 INFORMS Jaimungal [13], Cartea et al [14], Veraarta [59], Guilbaud and Pham [31], and Guéant et al [30] study minimizing the inventory risk and balancing the execution risk with consideration of microstructure of LOB. There are also order scheduling problems, especially when orders can be placed in different exchanges with different fee structures.…”