Premia pools disincentivize highly disruptive trades through size price impact.
After every transaction, the pool price level updates from
, depending on the size and the direction of the trade. This results in either an increased or decreased price for the next buyer/underwriter. There are no obvious reasons to disincentivize larger blocks of provided liquidity (on the LP side), however, whale-buying behavior needs to be accounted for.
Suppose a whale is waiting on the sidelines for the C-level to fall below their perceived market equilibrium, just to scoop up 50% of the pool's liquidity. Such a trade would cause a significant pool price level disruption; this disruption needs to be accounted for in the price charged to the whale. If the starting value is
, and the ending value (post whale trade) becomes
, what price impact penalty should be imposed on the whale?
In discrete form, the whale would end up paying
, however the differential form is slightly more accurate:
or more intuitively - the normalized step size, relative to the free capital in the pool.
Putting it all together, using
Ct∗=Ct adjusted for slippage
as a potential future trade-specific steepness modifier, we get a final pricing function: