Re-add Liquidity

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. .

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:

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

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."

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

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

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.

$UB_{F_{u}}=Fv_i$

2.3 Update Total Balance of the pool for each token

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

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