Open Access

Alexander Weiß

• In a recent paper, Alfonsi, Schied and Schulz (ASS) propose a simple order book based model for the impact of large orders on stock prices. They use this model to derive optimal strategies for the execution of large orders. We test this model in the context of an agent based microscopic stochastic order book model that was recently proposed by Bovier, \v{C}ern\'{y} and Hryniv. While the ASS model captures some features of real markets, some assumptions in the model contradict our simulation results. In particular, from our simulations the recovery speed of the market after a large order is clearly depended on the order size, whereas the ASS model assumes the speed to be given by a constant. For this reason, we propose a generalisation of the model of ASS that incorporates this dependency, and derive the optimal investment strategies. We show that within our artificial market, correct fitting of this parameter leads to optimal hedging strategies that reduce the trading costs, compared to the ones produced by ASS. Finally, we show that the costs of applying the optimal strategies of the improved ASS model to the artificial market still differ significantly from the model predictions, indicating that even the improved model does not capture all of the relevant details of a real market.