# Asymmetric, Concentrated Liquidity

ShadeSwap - The best Liquid Staking Derivative DEX in DeFi

Unlike centralized exchanges, Decentralized Exchanges (DEXs) are not based on a single centralized entity acting as custodians or intermediaries. Instead, traders on DEXs retain full control of their funds and private keys, and smart contracts execute trades for users in a neutral and automated fashion.

Most DEXs use Automated Market Maker (AMM) models to define the rules of trading, rather than relying on the order book model. An AMM algorithmically computes the price of the tokens inside a liquidity pool based on the supply and demand of the tokens in the liquidity pool. The allowed sizes for these liquidity pools can then be plotted onto a graph, forming a unique pricing curve. When you do a swap, the curve takes your inputted token amount and uses that to calculate what the other token's supply must be. Additionally, liquidity providers can deposit their tokens into liquidity pools in exchange for rewards coming from swap fees and token farming.

Automated Market Makers (AMMs) use mathematical formulas to automatically determine the price of assets in a liquidity pool based on supply and demand.

The allowed liquidity pool sizes for an AMM model can be referred to as a "curve."

## SilkSwap - *Asymmetric, Concentrated Liquidity*

*Asymmetric, Concentrated Liquidity*

ShadeSwap introduces for the first time a novel AMM model named, "SilkSwap." SilkSwap allows for customization over its curve, asymmetrically. To imagine this, take a look at the graph below:

SilkSwap is the first invariant to have customization over its configuration *asymmetrically*. Asymmetric configuration allows Shade Protocol to control the regions that are flat to concentrate liquidity, while also controlling the tail ends of the curve independently - allowing for modular control over when trades encounter price impact.

The green curve in Figure 1 above represents the SilkSwap invariant. Note that the left side of the equilibrium point has a wider, flat region - allowing for liquidity to concentrate where prices are expected to remain. Conversely, the right side of the equilibrium point has a shorter flat region where trades encounter price impact faster.

Even as the ratio of the liquidity pool changes significantly from the original market price, SilkSwap still allows traders to swap with low price impact. This is possible since SilkSwap decouples the price from the pool ratio. In other words, the math behind SilkSwap maintains a swap closer to the original market price allowing for the same price even when the pool ratio may have drastically changed. Therefore, the efficiency of SilkSwap is a combination of which side of the pool that you want to encourage/discourage, and the overall general balance of the pool.

SilkSwap allows for modular, asymmetric control over where liquidity is concentrated and how soon traders encounter price impact in any direction.

### Liquid Staking Derivatives (LSDs)

SilkSwap's asymmetric control over its curve allows for flexibility in any type of market. Specifically, SilkSwap excels in markets with asymmetric order flow. Using Liquid Staking Derivatives (LSDs) as an example, SilkSwap assumes that the price point of a staking derivative in a liquidity pool will not remain above the minting price point of the derivative for a long time. The reasoning behind this is because arbitrageurs would mint out the staking derivative and sell it for a premium on ShadeSwap, driving the price disparity back into harmony.

ShadeSwap has already displayed its power in its first week of launch. Osmosis, another DEX in the Cosmos Ecosystem, features a liquid staking derivative pool that is over 33x larger in liquidity than the same pool on ShadeSwap. However, with a trade that is 20% the size of the liquidity in the pool, Osmosis incurs price impact of ~25%, while ShadeSwap *only *incurs price impact of ~0.25% - making ShadeSwap 100x more efficient with 33x less liquidity.

ShadeSwap provides over 100x more efficiency than its competitors for Liquid Staking Derivative trading, even with significantly less liquidity.

## Comparison of Popular AMM Models

The X-axis represents the quantity of USDC tokens in the liquidity pool while the Y-axis represents the quantity of SILK tokens in the liquidity pool.

### Constant Product Market Maker (CPMM)

The orange curve above representing CPMM (Constant Product Market Maker) assumes that the product of the quantities of tokens in the liquidity pool is constant, which guarantees infinite liquidity inside the pool. The Constant Product invariant in its basic form assumes `X*Y=k`

, where `X`

and `Y`

are the supply of tokens in a pool and `k`

is the invariant. As users come to a DEX to trade in assets, the respective asset's balance in the pool increases which means that the asset it exchanged for *must *decrease - always maintaining the same product invariant.

CPMM works quite well for volatile tokens, as it promptly adapts the price in response to new trades. The parabolic shape and the "tails" of the curve on each end discourages large trades in the form of price impact. Price impact is used to keep liquidity providers safe, as their supplied tokens will never be at too much risk. The price impact of these large trades is essentially the trader’s cost paid to the liquidity provider for disrupting the ratio of the liquidity pool. Nevertheless, CPMM is not very suitable when trading low volatility or stable assets.

Constant Product Market Maker is great for pricing volatile assets & protecting liquidity providers in the form of price impact.

### Constant Sum Market Maker (CSMM)

The blue line in Figure 3 above represents the Constant Sum Market Maker (CSMM). This is another important AMM model conceptually. CSMM model assumes that the sum of the quantities of tokens inside the pool is constant. The Constant Sum invariant in its basic form assumes `X+Y=k`

, where `X`

and `Y`

are the supply of tokens in a pool and `k`

is the invariant. The advantage of this model is that any trade has zero price impact, which is a great property when swapping between fiat pegged stablecoins. However CSMM also has a pitfall that it allows for the complete drain of the entire liquidity inside the pool. For this reason, it is not used in practical applications.

Constant Sum Market Maker is great for pricing stable assets, but has no price impact to protect liquidity providers.

### Curve v2

The red curve in Figure 3 above represents "Curve v2". This model takes the benefits of CPMM and combines it with the benefits of CSMM. Curve v2 assumes that the two tokens' prices in the liquidity pool are expected to remain stable. When looking at Curve v2 and those alike, the flat region in the center of the curve represents the area where prices are expected to remain – allowing for liquidity providers to concentrate their liquidity in that region, making for more efficient trades.

Additionally, Curve v2 introduces the ability to have configuration control over the region where the curve is flat - allowing the curve to adapt precisely for different types of stable assets. However, as the curve is adjusted, each side *must symmetrically* adjust in unison - restricting Curve v2 from the advantages of having *asymmetric control *over the curve, as seen in SilkSwap.

Curve v2 combines the protection of liquidity providers from CPMM with the efficient pricing of stable assets from CSMM, but it is mathematically restricted by symmetrical control over its pricing curve.

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