# Liquidity (LP)

## Concentrated Liquidity

To boost capital efficiency, Oyster AMM employs the **concentrated liquidity approach.** Like concentrated liquidity for the spot market, each liquidity in Oyster AMM only supports trading in a specific price range.

LPs are only required to specify the width of the price range instead of the lower and upper price of the range. 

## Price Range and Capital Efficiency Boost

The most common definition of capital efficiency is to compare the value of assets required for the same trade size and the slippage. 

$$
CapitalEfficiencyBoost = \frac{x \cdot P\_c \cdot 2}{
x\_{\text{virtual}} \cdot P\_c \cdot (\alpha \cdot (1 + r\_i) - \sqrt{\alpha}) \cdot {\frac{\sqrt\alpha - 1}{\sqrt\alpha}}
} = \frac{2}{
\left( \sqrt{\alpha} \cdot (1 + r\_i) - 1 \right) \cdot \left({{\sqrt\alpha}-1} \right)
}
$$

<figure><img src="/files/z8UldSUHFQxSbpM8EElW" alt=""><figcaption></figcaption></figure>

The LP continues to receive fee income while the price is in the range.

If the AMM price goes out of the price range of concentrated liquidity, anyone could initiate the removal of that liquidity and convert that into a trading position, which goes to the account of the original owner of the concentrated liquidity. An execution fee is paid to the initiator of the removal transaction to compensate for the gas cost. Please refer to the [Pair Specification](https://docs.synfutures.com/docs/User-Guide/Pair-Specifications) section.

## Net position and margin requirement

When adding liquidity to Oyster AMM, a long position is created for the liquidity, and an offset short position is created for the LP. The sum of these two positions is the net position of the LP.

As the AMM price **deviates** from the price when concentrated liquidity is created, that liquidity would inherently have **an implied net position**, which can be calculated from the equation below. Each concentrated liquidity will always meet the margin requirement for the implied net position within its chosen price range. LPs are allowed to remove the liquidity from their concentrated liquidity anytime, and that is converted into a trading position the size of the implied net position and the remaining margin, along with any fees earned. After concentrated liquidity is removed and converted, the LP can then manage the trading position accordingly.

$$
NetPosition(P) = x\_{\text{virtual}} \cdot \left( \sqrt{\frac{P\_c}{P}}-1 \right), \text{ if } P \in \[P\_a, P\_b]
$$

Oyster AMM mandates that the liquidity maintains a sufficient margin to meet the initial margin requirement for the resulting net position at both price range boundaries. Please refer to the [whitepaper](https://www.synfutures.com/v3-whitepaper.pdf) for an in-depth discussion.

Relationship between supplied margin and liquidity provided.

$$
x\_{real} = \frac{M}{P\_c \cdot (\alpha \cdot (1 + r\_i) - \sqrt{a})}
$$


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