Optimal Order Exposure in a Limit Order Market

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 placement of limit and hidden orders. We obtain the analytical solution to this 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. Our analytical solutions together with numerical experiments suggest an optimal execution pattern that the trader should submit hidden orders at early stages, possibly turn to a mixture of limit and hidden orders later, and use limit orders only when the execution deadline is approaching