  Volume imbalance in a limit order book is often considered as a reliable
indicator for predicting future price moves. In this work, we seek to analyse
the nuances of the relationship between prices and volume imbalance. To this
end, we study a market-making problem which allows us to view the imbalance as
an optimal response to price moves. In our model, there is an underlying
efficient price driving the mid-price, which follows the model with uncertainty
zones. A single market maker knows the underlying efficient price and
consequently the probability of a mid-price jump in the future. She controls
the volumes she quotes at the best bid and ask prices. Solving her optimization
problem allows us to understand endogenously the price-imbalance connection and
to confirm in particular that it is optimal to quote a predictive imbalance.
Our model can also be used by a platform to select a suitable tick size, which
is known to be a crucial topic in financial regulation. The value function of
the market maker's control problem can be viewed as a family of functions,
indexed by the level of the market maker's inventory, solving a coupled system
of PDEs. We show existence and uniqueness of classical solutions to this
coupled system of equations. In the case of a continuous inventory, we also
prove uniqueness of the market maker's optimal control policy.
