As described in High-frequency volatility, 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.
Some definitions:
Large tick assets: Spread almost always equal to one tick
Small tick assets: Spread typically a few ticks
α: Tick size (minimum price variation)
S: Price of the asset
α/S: Relative tick size
σ: Volatility (typically intraday)
Too large a tick will generate too many bounces (alternations) and not many level changes (continuations)..
Too small a tick and the spreads might show flickering quotes and no trades (with an externality of processing quotes with low informational content).
These issues are examined in Large tick assets: implicit spread and optimal tick size and successfully tested in How to predict the consequences of a tick value change? Evidence from the Tokyo Stock Exchange pilot program.
The 2009 paper Volatility Estimation under Endogenous Microstructure Noise describes in details the estimation of eta.