Optimal Asset Liquidation Using Limit Order Book Information

We consider an asset liquidation problem at the market microstructure level, where we use limit order book information to construct a measure of the instantaneous supply and demand imbalance in the market. In this context, it is optimal to submit sell orders when this imbalance is low, indicating that a price drop is imminent. Identifying good trading times is equivalent to solving an optimal stopping problem, where the objective is to stop whenever the supply-demand imbalance is small. The solution to such an optimal stopping problem divides the state space into a "trade" and "no trade" region. We present structural properties of the optimal policy and use a dynamic programming formulation to find good approximations to the optimal trade region. We also investigate shapes of the trade and no trade regions given different underlying price processes, input parameters and assumptions on the latency of the trade execution. Finally, we calculate efficiently the cost of latency in the trade execution and demonstrate that the advantage of observing the limit order book can dissipate quickly as latency increases. In the empirical studies section, we show that our optimal policy significantly outperforms the benchmark TWAP algorithm in liquidating on-the-run U.S. treasury bonds, saving on average approximately 1/3 of the spread per share liquidated if trades are executed with low latency (~10 milliseconds)