Study examines market impact of small orders in futures contracts.
problem Understanding market impact of small orders in financial markets.
method Empirical study using tick data, normalizing results, proposing a simple linear model.
result Market impact of small orders is either linear or concave, depending on the instrument.
There are two schools of thought regarding market impact modeling. On the one hand, seminal papers by Almgren and Chriss introduced a decomposition between a permanent market impact and a temporary (or instantaneous) market impact. This decomposition is used by most practitioners in execution models. On the other hand,…
Study finds a crossover from linear to square-root market impact based on order volume.
problem Understanding the dynamics of market impact as a function of order volume.
method Used a large dataset of 8 million trades to establish the crossover between linear and square-root market impact regimes. Applied a dynamical theory of liquidity to explain the results.
result Quantitative agreement with data achieved by considering two liquidity time scales: fast and slow.
Study finds price impact is universal in anonymous markets.
problem Understanding price impact in anonymous electronic markets.
method Analysis of proprietary dataset and linear propagator model.
result Magnitude and time dependence of price impact are universal in anonymous markets.
Study hedging covered options with linear impact and gamma constraint.
problem Hedging covered options with linear market impact and gamma constraint.
method Stochastic target and partial differential equation smoothing techniques.
result Super-replication price is viscosity solution of a fully non-linear parabolic equation.
Using a proprietary dataset of meta-orders and prediction signals, and assuming a quasi-linear impact model, we deconvolve market impact from past correlated trades and a predictable return component to elicit the temporal dependence of the market impact of a single daily meta-order, over a ten day horizon in various e…
Modeling market impacts leads to perfect hedging strategies.
problem Trading with permanent market impacts and nonlinearity.
method Modeling market impacts using g-expectation and nonlinear stochastic integrals; introducing completeness condition for perfect replication.
result Under certain conditions, derivatives can be perfectly hedged dynamically.
Two models predict similar high-frequency price dynamics but differ in low-frequency impact strength.
problem Understanding the relationship between market prices and fundamental information.
method Comparing a microfounded linear model with a data-driven model at high and low frequencies.
result Both models predict similar high-frequency price dynamics but differ in low-frequency impact strength.
The study reveals how institutional trading activity impacts markets, finding that total order flow is key.
problem Understanding how institutional trading activity affects market impact.
method Analysis of a large database of metaorders by institutional investors in the U.S. equity market, using a simple heuristic model.
result The market impact of multiple metaorders depends on the total number of metaorders and their mutual sign correlation, reproducing empirical market impact curves.
Equity auctions show linear price impact up to a large volume, then non-linear.
problem Understanding price impact in equity auctions.
method High-quality data analysis of Paris stock exchange auctions.
result Price impact is linear up to a large volume, then becomes non-linear.
This paper deals with an optimal position management problem for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker's continuous trading incurs a stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC cou…
Decomposing market impact into diffusive components
problem Market impact scaling
method Decomposing impact into realized and counterfactual returns
result Implication of square-root law in information-neutral regime
Optimal trading strategy under market resistance and concave price impact model.
problem Optimal trading in a market with endogenous resistance and concave price impact.
method Modeling market resistance, deriving a stochastic Fredholm equation, proving existence and uniqueness, proposing an iterative scheme.
result Existence and uniqueness of optimal control under certain conditions, exponential convergence of iterative scheme.
Study Nash equilibria for risk-averse investors in a market with transient price impact.
problem Optimizing costs or maximizing expected utility for risk-averse agents in a market with transient price impact.
method Explicit representations and numerical analysis of Nash equilibria for mean-variance optimization and expected exponential utility maximization.
result Explicit representations and uniqueness of Nash equilibria for mean-variance optimization.
The paper examines how price impact influences optimal investment, demand, and arbitrage in a competitive market.
problem The impact of price impact on optimal investment, demand, and arbitrage in a competitive market.
method Analyzes the effects of price impact on optimal policies, pricing rules, and demand schedules for contingent claims.
result Price impact leads to constrained trading and non-linear hedging costs, affecting arbitrage opportunities and equilibrium positions.
Proposes a new model to measure trade impact and information content in fluctuating markets.
problem Measuring price impact and information content of trades in a time-varying market setting.
method Non-linear observation-driven model for dynamically estimating market impact and information content.
result Market impact shows intraday patterns with large fluctuations, some of which are exogenous.
We consider the problem of portfolio optimization in the presence of market impact, and derive optimal liquidation strategies. We discuss in detail the problem of finding the optimal portfolio under Expected Shortfall (ES) in the case of linear market impact. We show that, once market impact is taken into account, a re…
Study market impact using hedging derivatives to explain market behavior.
problem Understanding and explaining market impact in financial markets.
method Developed a perturbation theory of market impact using hedging derivatives and established a pricing equation.
result Established a relation between immediate and permanent impact in market impact.
New findings reveal non-linear price impact scaling across financial markets.
problem Understanding how stock prices move at higher frequencies.
method Analyzing aggregated trades on various intra-day scales.
result Price impact has a universal non-linear shape, varying little across instruments.
The study explains the concavity of price impact in markets.
problem The asymptotic concavity of price impact in meta-orders.
method A model with linear local price impact and co-directional trades.
result Volumes at best bid and ask prices favor the executor.
The study uncovers the complex interactions between stock market instruments and their impact on trading costs.
problem Underestimation of trading costs and contagion effects due to ignoring interactions between different order flows.
method Introduces a multivariate linear propagator model to describe the joint dynamics of assets and accounts for significant covariance of stock returns.
result The model successfully describes the sectorial structure of market correlations and accounts for a significant fraction of the covariance of stock returns.
Two models improve market impact analysis, especially for rare price changes.
problem Improving models to accurately capture market impact.
method Two-event framework, extending TIM and HDIM models.
result HDIMs outperform TIMs, capturing anti-correlation between returns and order flow.
This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we …
The paper uncovers two key laws of market impact influenced by volume and participation rate.
problem Understanding the roles of volume and participation rate in market price response.
method Extending the no arbitrage approach to include sophisticated market participants, deriving price dynamics from order flow dynamics.
result Recovery of two square root laws governing market impact.
In this paper, we assume that the permanent market impact of metaorders is linear and that the price is a martingale. Those two hypotheses enable us to derive the evolution of the price from the dynamics of the flow of market orders. For example, if the market order flow is assumed to follow a nearly unstable Hawkes pr…
Optimal liquidation model reduces trading costs in OTC markets.
problem Minimizing trading costs in Over-The-Counter markets.
method Developed an optimal portfolio liquidation model in Locally Linear Order Book framework.
result Optimal liquidation time is proportional to the square root of the traded volume.
Transient market impact explained via Nash equilibrium in a game.
problem Understanding the transient nature of market impact.
method Analyzing a game between a trader and an arbitrageur, deriving decay kernels.
result Implied transient impact can be derived from trader behavior at Nash equilibrium.
Investors' strategies in a market influenced by price impact are analyzed, showing aggressive behavior when impact exceeds a critical point.
problem Strategic interaction and Nash equilibria of investors in a financial market with price impact.
method Analysis of Nash equilibria for relative investors with CRRA and CARA utility functions in a Brownian motion-driven market, considering both linear and non-linear price impacts.
result Investors' aggressive behavior is observed when price impact exceeds a critical parameter.
Study optimal strategy for maximizing exponential utility in financial market with linear price impact.
problem Maximizing exponential utility in financial market with linear price impact.
method Purely probabilistic approach using duality.
result Computed optimal portfolio strategy and value for Ornstein-Uhlenbeck process.
The study extends a framework to analyze cross-impact in multi-asset markets.
problem Analyzing cross-impact and no-dynamic-arbitrage in multi-asset markets.
method Deriving theoretical limits for cross-impact from the condition of absence of dynamical arbitrage, testing these constraints with data.
result Significant violations of cross-impact symmetry found, but not exploitable due to bid-ask spread.
In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact in a multi-player framework by introducing strategic interactions into the Almgre…
Optimizes bidding in hourly and quarter-hourly electricity markets to reduce price impact.
problem Maximizing profit in two consecutive electricity markets with market impact and transaction costs.
method Examined multiple price scenarios, estimated market impact, used trading strategies, provided theoretical results.
result Minimizing price impact is more profitable than maximizing arbitrage in the German EPEX market.
DeepCausalMMM models marketing impacts using deep learning and causal inference.
problem Traditional MMM approaches struggle with non-linear dynamics and temporal patterns.
method Combines deep learning, causal inference, and marketing science. Uses GRUs for temporal patterns and DAG structure for channel dependencies.
result Captures non-linear dynamics and temporal patterns in marketing impacts.
We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a non-linear Black-Scholes Equation that provides an exact replication strategy. This equation is fully non-linear and singular, but we show that it is well posed, and we prove existence o…
We provide a microfoundation for linear price impact models in a stationary market.
problem Deriving linear price impact models in a stationary market with asymmetric information.
method Deriving linear price impact models as the equilibrium of an agent-based system.
result The model shows compatibility with universal price diffusion at small times and non-universal mean-reversion at larger times.
The asymmetric price impact between the institutional purchases and sales of 32 liquid stocks in Chinese stock markets in year 2003 is carefully studied. We analyze the price impact in both drawup and drawdown trends with consecutive positive and negative daily price changes, and test the dependence of the price impact…
Combines dynamic programming and neural networks for optimal portfolio execution in regime-switching markets.
problem Optimal execution in a market with multiple regimes and non-linear impact costs.
method Four-step numerical framework: approximated orthogonal portfolios, dynamic program for schedule, neural network optimization.
result Neural network optimized strategy outperforms traditional methods in both CRRA and mean-variance objectives.
An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. Thes…
The paper analyzes liquidity in decentralized finance, deriving impact functions and de-pegging risks.
problem Understanding and quantifying market impact and de-pegging risk in decentralized finance.
method Derives market impact functions for optimal-growth liquidity providers, views Constant Product Market Maker as a Carnot engine, and links de-pegging risks to catastrophe bonds.
result New insights into liquidity models and de-pegging risks in decentralized finance.
Model explains asset price dynamics, defaults, and market crashes via non-linear dynamics.
problem Understanding asset price dynamics, defaults, and market crashes in financial markets.
method Proposes a non-equilibrium model incorporating market frictions and feedback mechanisms.
result The QED model produces non-linear dynamics, broken scale invariance, and corporate defaults.
Study optimal execution in financial markets with constraints.
problem Optimal execution with non-negative constraints in a linear price impact model.
method Purely probabilistic approach via non-linear ODE.
result Complete characterization of value and optimal control.
Model quantifies market price of trading liquidity risk and market depth.
problem Analyzing the market price of trading liquidity risk and market depth.
method Introduced a framework to analyze market price of liquidity risk, derived inhomogeneous Bernoulli ODE, obtained closed form solutions.
result Market depth encapsulates the market price of liquidity risk.
We solve dynamic portfolio allocation with LQG for predictable markets.
problem Dynamic portfolio allocation with market predictability, price impact, and partial observability.
method LQG framework for linear state-space models, deriving optimal control policy.
result Existence and uniqueness of optimal controller linked to non-arbitrage criterion.
Solves VWAP liquidation under transient market impact.
problem Optimal liquidation with VWAP benchmark in a transient market.
method Analyzes linear and transient market impact, considers risk-averse investors with CARA utility, finds explicit solutions in continuous and discrete time.
result Explicit solutions found, optimal VWAP includes both buy and sell trades even with convex decay kernel.
Bayesian theory explains market impact of large trades.
problem Reduction of price impact from large trades.
method Bayesian approach incorporating all trade information.
result Recovery of market impact laws including square-root and linear regimes.
Extended model accounts for finite memory effects in financial markets.
problem Modeling latent liquidity and its impact in financial markets.
method Continuous reaction-diffusion setup with finite cancellation and deposition rates.
result Square root impact law with finite memory corrections and linear permanent impact.
By incorporating market impact and asymmetric sensitivity into the evolutionary minority game, we study the coevolutionary dynamics of stock prices and investment strategies in financial markets. Both the stock price movement and the investors' global behavior are found to be closely related to the phase region they fa…
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden, large variation of the spread, corresponding to a temporary crisis of liquidity in a double auction financial market. We find that the spread decays very slowly to its normal value as a consequence of the strategic limit order pl…