| Abstract: |
Trading large volumes of a financial asset in order driven markets requires
the use of algorithmic execution dividing the volume in many transactions in
order to minimize costs due to market impact. A proper design of an optimal
execution strategy strongly depends on a careful modeling of market impact,
i.e. how the price reacts to trades. In this paper we consider a recently
introduced market impact model (Bouchaud et al., 2004), which has the property
of describing both the volume and the temporal dependence of price change due
to trading. We show how this model can be used to describe price impact also
in aggregated trade time or in real time. We then solve analytically and
calibrate with real data the optimal execution problem both for risk neutral
and for risk averse investors and we derive an efficient frontier of optimal
execution. When we include spread costs the problem must be solved numerically
and we show that the introduction of such costs regularizes the solution. |