IMM Balancing Indicator

The current total value of the pool is:

We define the pool as balanced if Xc * rX = Yc* rY, i.e., the values of the LP token and ETH assets in the pool are equal.

So, we can determine the pool to be balanced if:

The parameter is used to measure the pool diversion from equilibrium state:

If q>1 there is a shortage of ETH.

If q>1 there is a shortage of ETH.

Function f(q) is used to adjust the Oracle price according to the pool state.

The parameters a, b are set on the following range:

0 <= b < 1

0 <= a < ∞

Due to solidity efficiency limitations, parameter “a” can only be set to values starting from 0 and increasing in 0.5 increments till infinity.

If q = 1, f(q) = 1, the pool is in equilibrium state and no adjustments are applied to the Oracle price.

If q>1, f(q) < 1, the pool is in shortage of ETH and the pool internal rate will be less than the Oracle price.

If q<1, f(q) > 1, the pool is in shortage of LP token and the internal rate will be higher than Oracle price.