# 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](https://app.gitbook.com/@pods-finance-1/s/teste/~/drafts/-MNH5EfMIG3zYkpvevUc/options-amm-overview/optionamm/pricing). . 

![ABPrice variable on \_addLiquidity at AMM.sol](/files/-MQu4nFlTcBWTvQd_jHa)

### 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](/files/-MQtoqSEnGAFHunBNDEQ)

![FImp function at AMM.sol](/files/-MQtqzKe4-6dxJBkTaVx)

### 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 ](/files/-MQsUEOVd0nNa05RUkSA)

### 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](/files/-MQtnKp-AcxlCkVXnPWV)

### 2.3 Update Total Balance of the pool for each token

$$TB\_{A\_{i}}=TB\_{A\_{i-1}} +A\_{du}$$ 

$$TB\_{B\_{i}}=TB\_{B\_{i-1}} +B\_{du}$$ 

{% hint style="info" %}
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)
{% endhint %}

![](/files/-MQtnZCGVSnCjA2K5iuJ)

{% hint style="success" %}
Re-add liquidity ✅
{% endhint %}


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