Add Liquidity

Understanding the add liquidity event step-by-step.

Add Liquidity

The event of 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 add liquidity function will perform the following activities:

1. Calculate factors

1.1 Calculate Option Price

This happens if $i≠0$. If $i=0$ , it is not required to calculate the option price in the very first liquidity provision in a pool.

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 for pricing the options, check this section.

ABPrice variable on _addLiquidity at AMM.sol

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

If $i=0$ , $F_{v_{i}}=1$

If $i≠0$ , $\displaystyle F_{v_{i}}= \frac{TB_{A_{i-1}}\cdot P_i+TB_{B_{i-1}}}{DB_{A_{i-1}} \cdot P_i+DB_{B_{i-1}}}$

Since this is the first liquidity provision of the pool, this is $i=0$ and therefore, $F_{v_{i}}=1$.

PoolValue factor variable on _addLiquidity at AMM.sol

FImp function at AMM.sol

2. Updates

2.1 Update Deamortized Balance of the pool for each token

By the time the pool is created ($i=0$) , the $DB_{A_i}$and $DB_{B_i}$ will be equal to the $A_{du}$ and $B_{du}$ since:

$F_{v_{i}} = 1$ $\displaystyle DB_{A_{i-1}}=0$ $\displaystyle DB_{B_{i-1}}=0$

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

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

deamortizedBalance on _addLiquidity at AMM.sol

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

Updating this factor is essential, especially when there is a re-add liquidity event.

$UB_{A_{u}}=A_{du}$

$UB_{B_{u}}=B_{du}$

The $UB_{f_{u}}$ works as if it was a snapshot of the pool's factor at the moment of this user's deposit. This factor will be updated in the case of re-add liquidity by the user.

$UB_{F_{u}}=F{v_{du}}$

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 the balanceOf() of the pool contract of the respective token (tokenA or tokenB)

Add liquidity ✅