Optimal trade execution under endogenous order flow

Abstract

We consider a novel portfolio liquidation model with self-exciting order flow in which a large investor’s trading activity has an impact of future order flow. We allow for both instantaneous and permanent market impact. Assuming that the investor is risk neutral and impact parameters are deterministic constants we solve the model in closed form. If the feedback of current trading on future order flow is not too strong, the optimal trading strategy is of hyperbolic form. If the feedback effect becomes too dominating, cyclic strategies may emerge and beneficial round trips may exist. We implement our model on 110 NASDAQ stocks. Our empirical analysis shows that as the level of endogeneity increases, our strategy delivers increasingly superior performance to the commonly employed TWAP strategy. The empirical analysis suggests that the feedback effect is always weak enough to exclude statistical arbitrage.

Keywords: Liquidity Risk, Optimal Trading Strategy, Portfolio Liquidation, Hawkes process

JEL Classification: G11