That's true that in market making papers, like Dealing with the Inventory Risk. A solution to the market making problem 2012 by Guéant, L and Fernandez-Tapia, the volatility is often taken as constant.
What does it means? indeed you have two nature of uncertainties on the table when you make the market:
- the mark to maket value of your inventory. from a quantitative viewpoint on market making, the volatility is the proxy that your inventories goes against you. The volatility is a way to mesure the expected value of your inventory in the future.
- the probability that other market participants will trade with you, that leads to two effects: it allows to reduce your inventory (reacting to an anticipation of risk, thanks to your expectation of the volatility), or it could inflate your inventory towards more imbalance in an undesired solution (this is typically measure the adverse selection risk, that very often practitioners call toxicity of the flow).
They are very different in nature. If you know something about future prices, for instance thanks to a calendar (some economic numbers will be disclosed during the trading day, at 14:30 for Europe, but you do not know if they will be positive or not): put this information in your volatility model. It will naturally tell to the optimizer that you have to reduce your inventory before 2.30pm.
If you have a directional information on the price, for instance a News has just been disclosed about a patent issued by a company (think about the announce of Pfizer 's covid vaccine), it is affecting the flow of other participants in the direction of the information: if your quotes do not adjust, they will be hit a bad way. They you have to put this in your model of the probability of being lifted (that is often an point process with asymmetric intensities on the bid and ask side).