arXiv · arXiv q-fin · 2024
This paper introduces a new algorithmic execution model that integrates interbank limit and market orders with internal liquidity generated through market making. Based on the Cartea et al.\cite{cartea2015algorithmic} framework, we incorporate market impact in interbank orders while excluding it for internal market-making transactions. Our model aims to optimize the balance between interbank and internal liquidity, r…
Yusuke Morimoto
arXiv · arXiv q-fin · 2018
The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated across stocks, and (ii) this correlation increases during the last few hours of the trading session. These observations could be attributed, in part, to the prevalence of portfolio tra…
Seungki Min, Costis Maglaras, Ciamac C. Moallemi
arXiv · arXiv · 2026
We address the problem of executing large client orders in continuous double-auction markets under time and liquidity constraints. We propose a model predictive control (MPC) framework that balances three competing objectives: order completion, market impact, and opportunity cost. Our algorithm is guided by a trading schedule (such as time-weighted average price or volume-weighted average price) but allows for deviat…
Thomas P. McAuliffe, Samuel Liew, Yuchao Li, Andrey Ushenin, Chihang Wang
arXiv · arXiv q-fin · 2023
Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This work studies optimal trading and statistical arbitrage in CPMs where balancing exchange rate risk and execution costs is key. Empirical evidence shows that execution costs are accur…
Álvaro Cartea, Fayçal Drissi, Marcello Monga
arXiv · arXiv q-fin · 2017
Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of the first three explanations. Empirical features of recent mini-flash crashes are present in our framework. For example, there are periods when no such events will occur. If they d…
Erhan Bayraktar, Alexander Munk
arXiv · arXiv q-fin · 2014
We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal solution is front loaded for concave impact and that its expected cost is significantly lower than that of conventional strategies.…
Gianbiagio Curato, Jim Gatheral, Fabrizio Lillo
arXiv · arXiv · 2012
Trading large volumes of a financial asset in order driven markets requires the use of algorithmic execution dividing the volume in many transactions in order to minimize costs due to market impact. A proper design of an optimal execution strategy strongly depends on a careful modeling of market impact, i.e. how the price reacts to trades. In this paper we consider a recently introduced market impact model (Bouchaud …
Enzo Busseti, Fabrizio Lillo
arXiv · arXiv q-fin · 2009
We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group prope…
Takashi Kato
arXiv · arXiv · 2024
Optimal execution is an important problem faced by any trader. Most solutions are based on the assumption of constant market impact, while liquidity is known to be dynamic. Moreover, models with time-varying liquidity typically assume that it is observable, despite the fact that, in reality, it is latent and hard to measure in real time. In this paper we show that the use of Double Deep Q-learning, a form of Reinforc…
Andrea Macrì, Fabrizio Lillo
arXiv · arXiv · 2020
We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both directions and at discrete points in time. We derive an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs. We also discuss severa…
Julia Ackermann, Thomas Kruse, Mikhail Urusov
arXiv · arXiv · 2026
Automated execution algorithms are organized into schedule-based and liquidity-seeking families. This paper concerns the first, whose members -- Time-Weighted Average Price (TWAP), Volume-Weighted Average Price (VWAP), Percentage of Volume (POV) and Implementation Shortfall -- are all model-based: each derives its decisions from an explicit model, forecast, schedule or control rule. We introduce Shadow-PPOV, a passiv…
Vincent Maciejewski
arXiv · arXiv · 2026
Price-level limit order book (L2) data reveal aggregate liquidity but not the ordered queue required by price--time priority. Passive-execution backtests can therefore depend on an unobserved cancellation-allocation rule even when observed prices, quantities, and trades are held fixed. We frame recovery of market-by-order histories from aggregate snapshots as a conditional partial identification problem: multiple his…
Riya Danait, Yuliana Zamora, Ioana Boier
arXiv · arXiv · 2026
We derive a mesoscopic model for optimal execution with limit orders that incorporates microstructural features of passive price impact. Our framework is based on two empirical observables: the approximately exponential decay of limit-order fill probabilities with distance from the midprice, and the short-term linear response of price changes to order flow imbalance. Combining these ingredients, we obtain a reduced-f…
Alexander Barzykin, Robert Boyce, Eyal Neuman, Sturmius Tuschmann
arXiv · arXiv · 2026
Trader-facing dynamic fees are increasingly proposed for automated market makers (AMMs), but historical data do not identify how order flow would respond: trader-facing fees do not vary, trader types are latent, and a replayed tape is not a sequential decision environment. We therefore construct a minimal closed-loop simulator in which the missing signal exists by construction: two constant-product pools repriced by …
Wen-Ting Wang
arXiv · arXiv · 2026
We present the first application of MAP-Elites, a quality-diversity algorithm, to trade execution. Rather than searching for a single optimal policy, MAP-Elites generates a diverse portfolio of regime-specialist strategies indexed by liquidity and volatility conditions. Individual specialists achieve 8-10% performance improvements within their behavioural niches, while other cells show degradation, suggesting opportu…
Robert de Witt, Mikko S. Pakkanen
arXiv · arXiv · 2025
Conventional models of matching markets assume that monetary transfers can clear markets by compensating for utility differentials. However, empirical patterns show that such transfers often fail to close structural preference gaps. This paper introduces a market microstructure framework that models matching decisions as a limit order book system with rigid bid ask spreads. Individual preferences are represented by a…
Yao Wu
arXiv · arXiv · 2025
This paper investigates optimal execution strategies in intraday energy markets through a mutually exciting Hawkes process model. Calibrated to data from the German intraday electricity market, the model effectively captures key empirical features, including intra-session volatility, distinct intraday market activity patterns, and the Samuelson effect as gate closure approaches. By integrating a transient price impac…
Konstantinos Chatziandreou, Sven Karbach
arXiv · arXiv · 2024
Bertsimas and Lo's seminal work laid the groundwork for addressing the implementation shortfall dilemma in institutional investing, emphasizing the significance of market microstructure and price dynamics in minimizing execution costs. However, the ability to derive a theoretical Optimum market order policy is an unrealistic assumption for many investors. This study aims to bridge this gap by proposing an approach th…
Simeon Kolev