With A new approach for the dynamics of ultra high frequency data: the model with uncertainty zones, Robert and Rosenbaum define a model for the behavior of the traded prices of an asset that is simple enough to be defined by a single parameter (η), but realistic enough to describe adequately securities from different asset classes (like stocks and futures):
In Microstructure Of A Central Limit Order Book In FX Futures, Marcos Carreira shows how different microstructure parameters can lead to very different statistics given the same price process, by running Monte Carlo with fixed (known) volatility for the efficient price and using different values for α and η, generating different traded prices:
This model and the framework for simulating the behavior of the traded prices can be used to predict the impact of choosing a particular tick size and also what would be an optimal tick size. More on the applications of this model on the Tick size page.