Optimal Execution of a VWAP Order: A Stochastic Control Approach

  title={Optimal Execution of a VWAP Order: A Stochastic Control Approach},
  author={C. Frei and Nicholas Westray},
  journal={Econometrics: Mathematical Methods \& Programming eJournal},
We consider the optimal liquidation of a position of stock (long or short) where trading has a temporary market impact on the price. The aim is to minimize both the mean and variance of the order slippage with respect to a benchmark given by the market volume‐weighted average price (VWAP). In this setting, we introduce a new model for the relative volume curve which allows simultaneously for accurate data fit, economic justification, and mathematical tractability. Tackling the resulting… Expand
Optimal VWAP Execution Under Transient Price Impact
We solve the problem of optimal liquidation with volume weighted average price (VWAP) benchmark when the market impact is linear and transient. Our setting is indeed more general as it considers theExpand
Optimal solution of the liquidation problem under execution risk
We consider an investor that trades continuously and wants to liquidate an initial asset position within a prescribed time interval. During the execution of the liquidation order the investor isExpand
A Closed-Form Execution Strategy to Target Volume Weighted Average Price
We provide two explicit closed-form optimal execution strategies to target VWAP. We do this under very general assumptions about the stochastic process followed by the volume traded in the market,Expand
Optimal Execution in Hong Kong Given a Market-on-Close Benchmark
This work introduces a stochastic control formulation to target such a median benchmark in an empirically justified model which takes the key microstructural features into account and concludes by providing a novel decomposition of the trading risk into that which is intrinsic to the median benchmark and that due to execution. Expand
Optimal execution in Hong Kong given a market-on-close benchmark
For stocks traded on the Hong Kong Exchange, the median of five prices taken over the last minute of trading is currently chosen as the closing price. We introduce a stochastic control formulation toExpand
A Closed-Form Execution Strategy to Target Volume Weighted Average Price
Two explicit closed-form optimal execution strategies to target volume weighted average price (VWAP) are provided, under very general assumptions about the stochastic process followed by the volume traded in the market, and they account for permanent price impact stemming from order-flow of the agent and all other traders. Expand
Optimal VWAP Tracking
We consider the problem of finding a strategy that tracks the volume weighted average price (VWAP) of a stock, a key measure of execution quality for large orders used by institutional investors. WeExpand
A Class of Optimal Liquidation Problem with a Nonlinear Temporary Market Impact
  • Jiangming Ma, Di Gao
  • Mathematics
  • 2020
We extend the self-exciting model by assuming that the temporary market impact is nonlinear and the coefficient of the temporary market impact is an exponential function. Through optimal controlExpand
Volume Weighted Average Price Optimal Execution
We study the problem of optimal execution of a trading order under Volume Weighted Average Price (VWAP) benchmark, from the point of view of a risk-averse broker. The problem consists in minimizingExpand
Incorporating Order-Flow into Optimal Execution
We provide an explicit closed-form strategy for an investor who executes a large order when market order-flow from all agents, including the investor's own trades, has a permanent price impact. TheExpand


Optimal slice of a VWAP trade
Abstract This paper derives a static optimal execution strategy of a VWAP trade, in which the optimal execution strategy can be calculated by an iteration of a single variable optimization, ratherExpand
Improving VWAP. Strategies: A Dynamical Volume Approach
In this paper, we present a new methodology for modelling intraday volume, which allows for a reduction of the execution risk in VWAP (Volume Weighted Average Price) orders. The results are obtainedExpand
Optimal control of execution costs
We derive dynamic optimal trading strategies that minimize the expected cost of trading a large block of equity over a fixed time horizon. Specifically, given a fixed block SM of shares to beExpand
Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation
A singular version with state constraints of the stochastic target problems studied in Soner and Touzi is considered, which provides a general framework for the pricing of contingent claims under risk constraints and a direct PDE characterization of the associated pricing function. Expand
Mean Variance Optimal VWAP Trading
VWAP is the Volume Weighted Average Price of traded stock over a defined period. It is a metric of trade execution quality used by institutional traders to minimize the execution cost of largeExpand
Optimal Trading with Stochastic Liquidity and Volatility
  • R. Almgren
  • Economics, Computer Science
  • SIAM J. Financial Math.
  • 2012
A Hamilton-Jacobi-Bellman equation is constructed for the optimal cost and strategy of mean-variance optimal agency execution strategies for varying risk aversion and these strategies adapt optimally to the instantaneous variations of market quality. Expand
No-dynamic-arbitrage and market impact
Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationshipExpand
Dam rain and cumulative gain
We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling such an asset and associated derivatives isExpand
Optimal VWAP Trading Under Noisy Conditions
This article proposes an empirically tractable way to incorporate intra-day noise into a VWAP trading rule. In volatile markets, news arrives unexpectedly and rapidly. This should influence aExpand
Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes
Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: stronglyExpand