Article2013

OPTIMAL EXECUTION OF A VWAP ORDER: A STOCHASTIC CONTROL APPROACH

65 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Risk and Portfolio Optimization

Abstract

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 optimization problem using a stochastic control approach, we derive and solve the corresponding Hamilton–Jacobi–Bellman equation to give an explicit characterization of the optimal trading rate and liquidation trajectory.

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References

2001Optimal execution of portfolio transactions 1998Optimal control of execution costs 1986A transaction data study of weekly and intradaily patterns in stock returns 1985An Investigation of Transactions Data for NYSE Stocks 1985An Investigation of Transactions Data for NYSE Stocks 2010No-dynamic-arbitrage and market impact 2004Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes 2005Direct Estimation of Equity Market Impact

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2016Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications 2016A Closed-Form Execution Strategy to Target Volume Weighted Average Price 2018Trading algorithms with learning in latent alpha models 2014VWAP Execution and Guaranteed VWAP 2018Algorithmic Trading, Stochastic Control, and Mutually Exciting Processes 2018Linear Quadratic Stochastic Control Problems with Stochastic Terminal Constraint

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