Re-add Liquidity

Re-adding liquidity is very similar to add liquidity function, except for how the UB is updated.

Re-add Liquidity

This event can only happen for users that provided liquidity before. The event of re-adding liquidity requires the following information from the user: 1. $A_{du}$ Amount of token A to be added 2. $B_{du}$ Amount of token B to be added 3. Owner

After the information was supplied, the re-add liquidity function will perform the following activities:

1. Calculate factors

1.1 Calculate Option Price

For simplicity, let's acknowledge that the option price is a function that required a $MarketData$ and an internal vector ($IV$) as input.

$P_i=f_p(IV_{i-1},MarketData_i)$

For more details about the pricing formula or its contract implementation, check this section. .

ABPrice variable on _addLiquidity at AMM.sol

1.2 Calculate the Pool's Value Factor ($F_{v_{i}}$)

Since the re-add liquidity happens in a given moment$i≠0$, $F_{v_{i}}$may not be equal to 1, so there should be a $F_{v_{i}}$calculation. The following formula will trigger the calculation:

$\displaystyle F_{v_{i}}= \frac{TB_{A_{i-1}}\cdot P_i+TB_{B_{i-1}}}{DB_{A_{i-1}} \cdot P_i+DB_{B_{i-1}}}$

FimpOpening variable on _addLiquidity function at AMM.sol

FImp function at AMM.sol

2. Updates

2.1 Update Deamortized Balance of the pool for each token

In this step, the AMM saves how much it owes the user at the current Pool Value Factor "expense."

$\displaystyle DB_{A_{i}}=DB_{A_{i-1}} +\frac{A_{du}}{F_{v_{i}}}$

$\displaystyle DB_{B_{i}}=DB_{B_{i-1}} +\frac{B_{du}}{F_{v_{i}}}$

deamortizedBalance on _addLiquidity at AMM.sol

2.2 Update the User Balances for each token and the Pool Factor previously calculated

Updating this factor represents combining both deposits considering the time each entered the pool. $\displaystyle UB_{A_{u}}=UB_{A_{u_{i-1}}}\cdot \frac {F_{v_{i}}}{UB_{F_{u}}}+A_{du}$

$\displaystyle UB_{B_{u}}=UB_{B_{u_{i-1}}}\cdot \frac {F_{v_{i}}}{UB_{F_{u}}}+B_{du}$

The $UB_{f_{u}}$ works as if it was a picture of the pool's factor at the moment of this user's deposit. This factor will be updated again whenever there is a re-add liquidity event by the same user.

$UB_{F_{u}}=Fv_i$

Updating User Balance (userDepositSnapshot) at _addLiquidity on AMM.sol

2.3 Update Total Balance of the pool for each token

$TB_{A_{i}}=TB_{A_{i-1}} +A_{du}$

$TB_{B_{i}}=TB_{B_{i-1}} +B_{du}$

At the contract level, an ERC20 transfer is happening. Total balance (TB) is just a mathematical representation. The Total balance is checked by consulting thebalanceOf() of the pool contract of the respective token (tokenA or tokenB)

Re-add liquidity ✅