Optimal Liquidity Trading

Abstract

We study optimal liquidity trading in a framework where trade size has a price impact. A liquidity trader wishes to trade a fixed number of shares within a certain time horizon and to minimize the mean and variance of the costs of trading. Explicit formulas for the optimal trading strategies show that risk-averse liquidity traders reduce their order sizes over time and execute a higher fraction of their total trading volume in early periods when price volatility increases or price sensitivity decreases. In the presence of transaction fees, numerical simulations suggest that traders want to trade more frequently when price volatility or price sensitivity goes up. In the multi-asset case, price effects across assets have a substantial impact on trading behavior, as does continuous-time trading.

JEL Classification: C61, D40, G12