It’s not that clear.
https://www.acsu.buffalo.edu/~keechung/MGF743/Readings/G4.pdf
Median volatility is slightly lower with the smaller tick size, and there is no
evidence of changes in the extent to which price changes are subsequently reversed
Now this is in real markets.
In my opinion, for us in PRUN, volatility will go down. Not up.
Why would people offering better prices sooner than they otherwise would have cause volatility to go up?
Another piece of information about tick sizes causing spreads to be tighter and causing them to collapse further
This analysis allows for a substantially
larger effective sample size as compared to before-versus-after studies of marketwide tick size reductions, and allows for separate examination of tick size increases
and decreases. The empirical results indicate that bid–ask spreads are decreased
by three to five cents per share with the smaller tick size and provide no evidence
of a reduction in liquidity.
Now this is just one paper, thankfully done before electronic trading and HFT was systemic. But it puts some data points here.
This is why stocks well, A) do splits, but B) have specific tick sizes they operate in. That’s why Tesla doesn’t trade at $297.17573845834587. You pick a point relative to the volatility where you limit the precision of orders. Otherwise people will cluster up at one point and artificially keep the spread wide. When you want the spread to be narrow and tight, a healthy market.