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Stable Pools are tailored for tokens pegged to specific values, synthetics like liquid-staking derivatives, or assets correlated with others. This category encompasses stablecoins, synthetic or wrapped assets, and staked derivatives (e.g., staked Aptos and Aptos). These pools facilitate low-impact, low-fee exchanges between assets converging on a relative value of "1".

Stable Pool Math

To accommodate swaps between similar assets, Stable Pools utilize a distinct equation. Meridian employs a Stable Pool invariant (originally developed by Curve), which is as following:

Amplification Factor

Stable pools can be fine-tuned using an "amplification factor" (A), which influences trade price impact. This factor determines how closely the pool's trading curve aligns with either the constant product or constant sum curve. A low amplification factor makes the pool's assets more susceptible to deviating from their peg, while a high factor requires significant trade volumes to shift relative asset values. It's worth noting that maximizing this factor isn't always optimal, as it can affect fee accumulation in the presence of alternative markets for similar assets.

• Low Amplification Factor: In a pool with a low amplification factor, even small trades can cause noticeable deviations from the peg, making the pool less stable. Low A-factor is more suited for asset pairs that are less tightly correlated.

• High Amplification Factor: A high amplification factor makes the pool more resistant to price deviations. For example, swapping between dollar-pegged stablecoins in a pool with a high amplification factor would result in minimal price impact, even for larger trade sizes.

Pool Parameters

The pool creator initially sets the amplification factor, which can only be modified subsequently through protocol governance. Any intended changes to this factor over time require the submission of a governance proposal.

What are Weighted Pools?

Meridian's Weighted Pools operate by enforcing a Constant Weighted Product invariant for token swaps. A subset of these, known as liquidity bootstrapping pools, caters to auction-like mechanisms. These pools employ Weighted Math, making them versatile for a wide array of applications, including asset pairings without price correlation (e.g., ETH-USDC).

Unlike conventional x*y=k pools which are limited to 2 tokens of equivalent weights (50/50) , Meridian's weighted pools offer flexibility in token counts and proportions. Users can create pools with different weightings such as 80/20 or 60/20/20, among others. Available pairs are dictated by the standard combination formula below:

Meridian supports weighted pools with up to 4 total assets. As each asset within a pool can be traded against any other, the number of available swaps grows exponentially - reaching up to * pairs for pools with the maximum number of _ tokens. This proliferation of swap pairs naturally encourages increased trading activity, thereby boosting fee collection and distribution to liquidity providers.

Impermanent Loss

Weighted pools offer flexibility in how assets are weighted against each other, allowing liquidity providers to adjust the proportion of each token in the pool. As the token weight increases in favor of one asset, it significantly reduces the unrealized impermanent loss. For example, Impermanent loss decreases in a two-token pool as the asset weight changes, relative to price fluctuations between the tokens.

However, while weighted pools help minimize impermanent loss, they also introduce trade-offs in terms of price slippage. In pools where one token is heavily weighted, swaps experience higher slippage due to the reduced liquidity of the less weighted asset. To balance the reduction in impermanent loss with adequate liquidity, an 80/20 weighting ratio is commonly recommended.