Optimal Execution with Hidden Orders Under Self-Exciting Dynamics

Hidden liquidity is attracting significant volume share in modern order-driven markets, providing exposure risk reduction and mitigating adverse selection risk. In a continuous-time framework, we show there is a switching in the optimal liquidation strategy for a risk-neutral agent who uses both hidden and displayed limit orders controlling the order sizes. When market order arrivals are modeled as the Poisson process, we derive a closed-form solution that contains a switching time, at which the agent changes from a pure-hidden-order phase to a mixed-orders phase until termination. Under the Hawkes process with self-exciting dynamics, a numerical solution is provided. We show that the optimal strategy exhibits a similar two-phase pattern, except that the switching time becomes a function of the market order intensity. Simulation experiments show that the use of hidden order reduces liquidation cost, accompanied by an increase in liquidity. Given event-level limit order book data of 100 NASDAQ stocks, we test the liquidation strategies, where our strategy (with mixed type under the self-exciting dynamics) leads to cost reduction up to 57% to the pure limit order strategy and 15% to the strategy with both order types under the Poisson process