Optimal order execution using hidden orders

Hidden orders are offered by many lit trading venues for participants to hide the true size of their orders. To help a risk-neutral trader executing a target volume to minimize the execution cost by benefitting from the setting of a limit order market allowing hidden orders, we propose a multi-stage dynamic programming model to determine the optimal trading strategy involving hidden orders. We consider two settings, where in the first setting the trader uses market and hidden orders, and in the second setting the trader uses limit and hidden orders in intermediate periods and market orders at the final stage. In both settings, we derive analytical solutions to the dynamic programming model under certain assumptions and discuss economic implications of our results. We use order-message data from NASDAQ to estimate the model parameters and demonstrate the generality of our assumptions.