The Simulation Analysis of Optimal Execution Based on Almgren-Chriss Framework

Abstract

First, we compute the optimal execution strategy under the Almgren-Chriss framework, based on the assumption that the asset price follows the arithmetic Brownian motion with the linear impact function. On this basis, we discuss the price impact under the execution strategy with the parameter κ, and find that the trajectory becomes steeper as the parameter κ increasing. In the simulation analysis, we use the Brown Bridge to construct three asset price generation processes, and we compare the execution strategy between the Almgren-Chriss framework and the TWAP (The Time Weighted Average Price) strategy. The result shows that the TWAP strategy is superior to the AC strategy under an upward price trend, the two strategies have the same performance without price trend, and the AC strategy is better than the TWAP strategy under a downward price trend.