Optimal Execution of a Vwap Order: A Stochastic Control Approach

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.

Trading algorithms with learning in latent alpha models

“…Because there is limited liquidity at the best bid or ask price (the touch), the investor must “walk the book” starting at the bid (ask) and buy (sell) her assets at higher (lower) prices as she increases the size of each of her MOs. For tractability, and as Frei and Westray () (among others) note, a linear model for this “temporary price impact” fits the data well, and adding in concavity, while empirically more accurate, does not improve the R 2 beyond 5%. Hence, here we adopt a linear temporary price impact model and write the execution price as where controls the asset's liquidity, and hence the impact of trades.…”

Smart TWAP Trading in Continuous-Time Equilibria

“…This section relies heavily on the analysis in Frei and Westray (2015). The càdlàg process γ = (γ t ) t∈[0,1] is a gamma bridge process with γ 0 = 0 and γ 1 = 1 with probability one.…”

Optimal VWAP Execution Under Transient Price Impact

“…Among the exceptions, Refs. [18,20,16,11] considered the VWAP, but the price impact model used is the one of Almgren and Chris (with or without stochastic market volume).…”