Optimal execution strategies in limit order books with general shape functions

By Aurélien Alfonsi, Antje Fruth, Alexander Schied. 2007

436 citations recorded by the source corpus.

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modelling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e. of the volume of the LOB, or the exponential recovery of the bid–ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy of a risk-neutral investor, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/a918045bcc4162f436f2e31e13ded92916dea235

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

Citations in the corpus

Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis (2013, background): “can be very impatient), – trade with relatively large orders, even once their meta orders have been split thanks to an optimal trading scheme (like in [2,4,6] or [21]).”
Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016, positive): “, the terminal inventory XT is constrained to achieve the target H, then α ∗,S is zero: we retrieve the result that the optimal trading rate does not depend on the price process when it is a martingale, see [1], [33].”
A probabilistic weak formulation of mean field games and applications (2013, background): “Note that dPn(β)/dP are bounded in L(P ) for any p ≥ 1 and that the integrands above are bounded in L(P ) for any p ∈ [1, 2), by (F.”
Price Dynamics in a Markovian Limit Order Market (2011, background): “The dynamics of prices in such markets are not only interesting from the viewpoint of market participants –for trading and order execution (Alfonsi et al. (2010), Predoiu et al. (2010))– but also from a fundamental perspective, since they provide a rare glimpse into the dynamics of supply and demand”
PORTFOLIO LIQUIDATION IN DARK POOLS IN CONTINUOUS TIME (2012, neutral): “, Bertsimas and Lo [1998], Almgren and Chriss [2001], Almgren [2003], Obizhaeva and Wang [2006], Schied and Schöneborn [2009], Alfonsi et al.”
Statistical Modeling of High-Frequency Financial Data (2011, background): “…important issue for applications is the impact of orders on prices: the optimal liquidation of a large block of shares, given a ﬁxed time horizon, crucially involves assumptions on price impact (see Bertsimas and Lo [11], Almgren and Chriss [2], Obizhaeva and Wang [50], Alfonsi and Schied [1]).”
Incorporating order-flow into optimal execution (2016, positive): “In this setup the impact of the MO is temporary and only affects the price received by the trader who sent the MO, and, moreover, the LOB recovers infinitely fast to its state previous to the arrival of the MO, see [1,2,19,21,24,26] for further discussions and generalizations to relax the resilience”
Adaptive Execution: Exploration and Learning of Price Impact (2012, positive): “In light of this, academics and practitioners have devoted significant attention to the topic [Bertsimas and Lo [1998], Almgren and Chriss [2000], Kissell and Glantz [2003], Alfonsi et al. [2010], Moallemi et al.”
Optimal order placement in limit order markets (2012, background): “In one stream of literature (see Obizhaeva and Wang (2005), Alfonsi et al. (2010), Predoiu et al. (2011)) a trader is restricted to using market orders whose execution costs are given by an idealized order book shape function. Another approach is to model the process through which an order is filled”
Optimal Basket Liquidation for CARA Investors is Deterministic (2010, neutral): “[2, 3, 4, 5], to mention only a few.”
TRADING WITH SMALL PRICE IMPACT (2014, neutral): “, [6, 2, 30, 24, 44, 1, 48, 22] and the references therein.”
Designating Market Maker Behaviour in Limit Order Book Markets (2015, methodology): “optimal execution has been considered in the past in the models of Obizhaeva and Wang [2012] and Alfonsi et al. [2010]. However, these models generally considered resilience to be constant or have a very simple parametric form.”
A Stochastic Model for Order Book Dynamics (2010, positive): “At the level of applications, such models provide a quantitative framework for investors and trading desks to optimize trade execution strategies Alfonsi et al. (2007), Obizhaeva and Wang (2006). An important motivation for modelling high-frequency dynamics of order books is to use the information o”