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In a recent paper, Alfonsi, Fruth and Schied (AFS) propose a simple orderbook based model for the impact of large orders on stock prices. They use thismodel to derive optimal strategies for the execution of large orders. We applythese strategies to an agent-based stochastic order book model that wasrecently proposed by Bovier, \v{C}ern\'{y} and Hryniv, but already thecalibration fails. In particular, from our simulations the recovery speed ofthe market after a large order is clearly dependent on the order size, whereasthe AFS model assumes a constant speed. For this reason, we propose ageneralization of the AFS model, the GAFS model, that incorporates thisdependency, and prove the optimal investment strategies. As a corollary, wefind that we can derive the ``correct'' constant resilience speed for the AFSmodel from the GAFS model such that the optimal strategies of the AFS and theGAFS model coincide. Finally, we show that the costs of applying the optimalstrategies of the GAFS model to the artificial market environment still differsignificantly from the model predictions, indicating that even the improvedmodel does not capture all of the relevant details of a real market.

Executing large orders in a microscopic market model