The paper analyzes optimal liquidation strategies for cryptocurrencies considering both temporary and permanent price impacts.
problem Optimal liquidation strategies for cryptocurrencies in the presence of price impacts.
method Analytical and numerical solutions, including finite differences and optimal policy iteration.
result Optimal liquidation policies vary based on the functional form of temporary and permanent price impacts.
Optimal strategy for liquidating portfolios under discrete time intervals.
problem Optimizing liquidation of portfolios with discrete time constraints and impact effects.
method Modeling portfolio liquidation with N risky assets, using VaR for cost measurement, and deriving an optimal liquidation time.
result The optimal liquidation time is only influenced by temporary price impacts, not permanent ones.
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…
In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The mode…
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,…
Two strategic agents track their portfolios, influencing each other's trading targets.
problem Strategic competition in portfolio tracking with price impact.
method Stochastic linear quadratic differential game with terminal state constraints.
result Unique open-loop Nash equilibrium strategies emerge based on price impact types.
Optimizes liquidations in decentralized finance to manage credit risk.
problem Managing and liquidating positions in decentralized finance exchanges.
method Formulated as an ergodic optimal control problem, derived closed-form solutions for optimal liquidation strategies.
result Closed-form solutions balance immediate executions with price impacts and long-term rewards.
Modeling equity market impact with Chinese data, improving on existing models.
problem Understanding and quantifying market impact in Chinese equity markets.
method Developed a price impact model considering heteroscedasticity and dependency between permanent and temporary impacts using large tick data.
result The model outperforms existing models and suggests a constant impact exponent of around 0.7 across all stocks.
We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e., the impact per share of large metaorders is smaller than that…
In this comment we discuss the problem of reconciling the linear efficiency of price returns with the long-memory of supply and demand. We present new evidence that shows that efficiency is maintained by a liquidity imbalance that co-moves with the imbalance of buyer vs. seller initiated transactions. For example, duri…
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.
Study compares static vs adaptive strategies in two trading models.
problem Optimal execution in static vs adaptive strategies.
method Discrete and continuous time models with permanent and temporary impact.
result Static strategies are nearly as optimal as adaptive ones in the studied models.
Study optimal liquidation in uncertain timeframes, minimizing risk and costs.
problem Minimizing risk and costs in liquidating assets with uncertain termination.
method Analyzes three scenarios using Almgren-Chriss model, verifies viscosity solutions for HJB equation.
result Characterizes value function as unique viscosity solution of HJB equation.
Optimizes Ethena's yield strategy by controlling stETH and ETH futures positions.
problem Maximizes Ethena's yield while managing price impacts.
method Formulates and solves stochastic control problems for Ethena's yield-generating strategy.
result Explicitly determines optimal control rates for stETH and ETH futures.
Investigates optimal execution under time-varying liquidity, preventing price manipulation.
problem Optimal execution with time-varying liquidity impacts and price manipulation prevention.
method Almgren-Chriss framework, deterministic time variation, well-posedness, second-order conditions, price manipulation prevention.
result Sufficient conditions for a unique solution and prevention of price manipulation.
The paper solves portfolio liquidation under transient price impact for 100 NASDAQ stocks.
problem Determining optimal trading strategies under various market impact models.
method Derives explicit solutions for market impact parameters in a portfolio liquidation model.
result The derived strategy achieves significant cost savings compared to benchmark models.
The study examines how brokers' identity affects their trading strategies on the Toronto Stock Exchange.
problem Impact of anonymous trading on brokers' optimal execution strategies.
method Formulated a stochastic differential game and mean-field game to analyze the optimal execution problem of anonymous and identity-revealed trading.
result Obtained a closed-form solution for the optimal strategy under Almgren-Chris price impact framework.
The paper analyzes optimal stock position-building strategies in competitive markets.
problem Optimal stock position-building in competitive markets with market impact.
method Developed a game-theoretic framework to find best-response strategies.
result Closed-form solutions for equilibrium trading strategies were derived.
For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus…
Study price impact in OTC credit index market without order book.
problem Estimate price impact in OTC credit index market with no order book.
method Applied propagator technique to classify trades and correct for errors.
result Price impact is mainly permanent in OTC credit index market.
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition fulfilled by the corresponding value function and show its first regularity property…
Paper formulates optimal trading in a Mean Field Game with multiple traders.
problem Optimal trading in a market with multiple strategic traders.
method Formulates a Mean Field Game (MFG) to model interactions among multiple traders.
result Provides a closed-form solution for optimal trading in a MFG of controls.
Study optimal liquidation in markets with hidden information and price effects.
problem Optimal liquidation in markets with hidden bid prices and price impact.
method Model market dynamics, use stochastic filtering, and solve stochastic control problem for PDMPs.
result Derive optimality equation and continuous viscosity solution for value function.
We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and t…
Paper uses RL to optimize trading in time-varying liquidity markets.
problem Optimal execution in dynamic liquidity markets.
method Double Deep Q-learning for neural networks.
result Trained RL algorithm learns optimal trading policies in time-varying liquidity.
Paper solves optimal portfolio deleveraging with cross asset impacts.
problem Maximize equity while meeting debt/equity requirement with cross asset price impacts.
method Developed successive convex optimization (SCO) and an effective global algorithm integrating SCO, convex relaxation, and branch-and-bound.
result Proposed algorithms find global optimal solutions efficiently.
While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective i…
Optimizes trading co-integrated assets considering price impact and informational advantage.
problem Executing a basket of co-integrated assets with price impact.
method Optimal stochastic control problem, closed-form solution, verification theorem.
result Improves trading strategy by including additional assets, outperforming existing models.
Study optimal trading strategies with small price impacts.
problem Optimal portfolio selection in a model with temporary and transient price impacts.
method Derive explicit formulas for asymptotically optimal trading rates and performance losses in the large-liquidity limit.
result Losses are governed by volatility of frictionless target strategy, but optimal portfolio exploits price displacement.
Modeling cross-impacts between stocks with a two-component price impact model.
problem Understanding cross-impacts between stocks in a correlated market.
method Introducing self- and cross-impact functions, modeling average cross-response functions, fixing impact function parameters, and quantifying time lag impacts.
result Cross- and self-correlators are connected with cross-responses, and time lag impacts are divided into temporary and permanent components.
Optimal execution strategy for market and limit orders with speed limits and uncertainty.
problem Optimal execution of limit and market orders with trade speed limits and uncertainty.
method Continuous-time model with stochastic control problem, incorporating trade speed limiter and trader director.
result Identification of optimal dynamic trading strategies and conditions for optimality.
Study on HFTs' interactions with a large trader using mean field game theory.
problem Interactions between high-frequency traders and a large trader executing assets at discrete times.
method Modeling HFTs' behavior using a jump process and solving the equilibrium through mean field game approach.
result Inventory-averse HFTs lower LT's costs when market impact is large.
Investigates optimal trading strategies for illiquid assets using a modified market impact model.
problem Optimizing investment behavior in a large unregulated financial institution with illiquid assets.
method Extension of Almgren-Chriss model to account for market illiquidity and expected utility optimization.
result Explicit closed-form solution for optimal trading strategy with interesting properties.
Study improves prediction of commodity futures using multi-factor model.
problem Improving accuracy in predicting commodity futures prices.
method State-space functional regression model incorporating yield curve dynamics.
result Functional regression model outperforms Schwartz-Smith model in estimating short-end of futures curve.
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.
We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity so…
Optimal trading strategy adapts to signals in markets with price impact.
problem Optimal liquidation in markets with linear price impact and predictive signals.
method Formulated as a stochastic control problem, solved using probabilistic and convex analytic techniques.
result Explicit solution for optimal trading strategy in terms of SDEs.
This study examines how market makers balance risk and impact in foreign exchange markets.
problem Balancing risk management with market impact in foreign exchange markets.
method An intermediate scenario approach considering both instantaneous and permanent market impact components.
result Transient market impact is more prevalent than previously thought, challenging traditional market impact models.
New method accurately reconstructs Russell 3000 index, revealing crowded portfolios.
problem Crowding in index portfolios during reconstitution events.
method Developed a Python package for accurate index reconstruction using CRSP US Stock data.
result Annual Russell 3000 portfolios are more crowded than quarterly ones, suggesting lower transaction costs.
Algorithmic traders optimize execution and arbitrage in markets with hidden information.
problem Optimal execution and statistical arbitrage in markets with latent factors.
method Solve a large stochastic game with mean-field game limit, using convex analysis and FBSDE.
result Prove the MFG equilibrium is an ε-Nash equilibrium for finite player games.
Study on optimal trading in a finite population with market frictions and asymmetric information.
problem Optimal trading in a finite population with market frictions and asymmetric information.
method Investigates stochastic differential games with asymmetric information and market frictions, proving existence and uniqueness of Nash and Stackelberg-Nash equilibria.
result Existence and uniqueness of Nash and Stackelberg-Nash equilibria in both unconstrained and constrained trading scenarios.
RL agent outperforms model-based approach in detecting price manipulation.
problem Detecting and exploiting price manipulation opportunities.
method Compared model-free RL with model-based approach in a market with Almgren-Chriss framework.
result RL consistently outperforms model-based approach, especially with noisy parameter estimates.
We study the market impact of a meta-order in the framework of the Minority Game. This amounts to studying the response of the market when introducing a trader who buys or sells a fixed amount h for a finite time T. This perturbation introduces statistical arbitrages that traders exploit by adapting their trading strat…
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.
The paper constructs optimal hedging strategies for options with price impact.
problem Optimal hedging strategies for options with temporary price impact.
method Combining analytic and probabilistic tools to establish feedback representation of the optimal strategy and derive utility indifference price.
result Explicit asymptotic expansion of utility indifference price quantifying price impact.
Optimizes liquidation strategies for assets with Levy process price dynamics.
problem Maximizing cash received from asset sale with price impact.
method Almgren-Chriss framework, constant absolute risk aversion, Levy process approximation.
result Explicit expression for optimal liquidation trajectories.
Study models market volatility with persistent and temporary impacts.
problem Microstructure of rough volatility models driven by Poisson measures.
method Existence and uniqueness of solutions for stochastic path-dependent Volterra equations.
result Volatility process converges to fractional Heston model with spikes.
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.