Journal ArticleDOI
Optimal execution with nonlinear impact functions and trading-enhanced risk
TLDR
In this paper, the authors consider the problem of liquidating a large single-asset portfolio to minimize a combination of volatility risk and market impact costs, with an arbitrary positive exponent.Abstract:
Optimal trading strategies are determined for liquidation of a large single-asset portfolio to minimize a combination of volatility risk and market impact costs. The market impact cost per share is taken to be a power law function of the trading rate, with an arbitrary positive exponent. This includes, for example, the square root law that has been proposed based on market microstructure theory. In analogy to the linear model, a ‘characteristic time’ for optimal trading is defined, which now depends on the initial portfolio size and decreases as execution proceeds. A model is also considered in which uncertainty of the realized price is increased by demanding rapid execution; it is shown that optimal trajectories are described by a ‘critical portfolio size’ above which this effect is dominant and below which it may be neglected.read more
Citations
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Journal ArticleDOI
Optimal trading strategy and supply/demand dynamics
Anna A. Obizhaeva,Jiang Wang +1 more
TL;DR: In this paper, the authors develop a general framework for a limit order book market to capture the dynamics of supply/demand, and show that the optimal strategy to execute an order does not depend on the static properties of supply and demand such as bid-ask spread and market depth, it depends on their dynamic properties such as resilience: the speed at which supply or demand recovers to its steady state after a trade.
Direct Estimation of Equity Market Impact
TL;DR: In this article, the authors analyzed a large data set from the Citigroup US equity trading desks, using a simple but realistic theoretical framework, and fit the model across a wide range of stocks, determining the dependence of the coecients on parameters such as volatility, average daily volume, and turnover.
Journal ArticleDOI
Optimal execution strategies in limit order books with general shape functions
TL;DR: In this article, optimal execution strategies for block market orders placed in a limit order book (LOB) are derived for a general shape of the LOB defined via a given density function, allowing for empirically observed LOB shapes and obtaining a nonlinear price impact of market orders.
Posted Content
Optimal execution strategies in limit order books with general shape functions
TL;DR: This work builds on the resilience model proposed by Obizhaeva and Wang (2005) but allows for a general shape of the LOB defined via a given density function, and obtains a new closed-form representation for the optimal strategy of a risk-neutral investor.
Journal ArticleDOI
Optimal trade execution under geometric brownian motion in the almgren and chriss framework
Jim Gatheral,Alexander Schied +1 more
TL;DR: In this paper, the HJB equation is solved explicitly to find a closed-form solution for the optimal trade execution strategy in the Almgren-Chriss framework assuming the underlying unaffected stock price process is geometric Brownian motion.
References
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Journal ArticleDOI
Coherent Measures of Risk
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
Journal ArticleDOI
Optimal execution of portfolio transactions
Robert Almgren,Neil Chriss +1 more
TL;DR: In this paper, the authors consider the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact, and they explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty.
Journal ArticleDOI
The Components of the Bid-Ask Spread: A General Approach
Roger D. Huang,Hans R. Stoll +1 more
TL;DR: In this article, a simple time-series market microstructure model is constructed within which existing models of spread components are reconciled, and two alternative extensions of the simple model are developed to identify all the components of the spread and to estimate the spread at which trades occur.
Journal ArticleDOI
Inferring the Components of the Bid-Ask Spread: Theory and Empirical Tests
TL;DR: In this article, the relationship between the quoted bid-ask spread and two serial covariances, the serial covariance of transaction returns and the serial correlation of quoted returns, is modeled as a function of the probability of a price reversal, 7r, and the magnitude of price change, a, where a is stated as a fraction of the quoted spread.