Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions

Abstract

We study optimal liquidation of a trading position (so-called block order or metaorder) in a market with a linear temporary price impact (Kyle, 1985). We endogenize the pressure to liquidate by introducing a downward drift in the unaffected asset price while simultaneously ruling out short sales. In this setting the liquidation time horizon becomes a stopping time determined endogenously, as part of the optimal strategy. We find that the optimal liquidation strategy is consistent with the squareroot law which states that the average price impact per share is proportional to the square root of the size of the meta-order (