iZiSwap & Discrete Liquidity Model: Revealing the Future Trend of AMM

History of AMM

At the end of 2018, Uniswap was born out of nowhere. Instead of using order books like other DEXs at the same time, it adopted the AMM automatic market maker model to combat the limitations of Ethereum’s performance, including slow transaction confirmation speed. series of questions. Uniswap has proved the possibility of AMM in practice time and time again, and at the same time, the trade-off in performance has also brought many problems, such as inevitable slippage and impermanent loss, and the defects of low capital efficiency have also been criticized, and appear from time to time The sandwich attack and the poor user experience brought about by a single order type.

In May 2020, Uniswap v2 was launched, which added currency exchange on the basis of v1, and made it more difficult to manipulate prices. This seems more like a check for v1 and no optimization and adjustment of the AMM model . So one year later, in May 2021, the Uniswap team launched Uniswap v3, introducing the familiar aggregation liquidity solution.

Specifically, in v1 and v2, when LP provides liquidity to a certain liquidity pool, the liquidity will be allocated in all price ranges of (0, ∞). And most assets will only trade within a certain price range, so a large portion of the liquidity provided by LPs is never used, making capital rather inefficient. The aggregated liquidity scheme of v3 allows LP to choose the price range for providing liquidity, and only when assets are traded within the price range selected by LP, LP can get fee rewards. This approach increases AMM's capital efficiency to unprecedented heights. In contrast, slippage and impermanence losses have also been alleviated to a certain extent.

While Uniswap v3 solves the biggest current capital efficiency problem of AMMs, there are still some other problems waiting to be solved. Two years have passed since Uniswap v3 went live, and we have reason to wonder whether the Uniswap team is preparing for Uniswap v4. While looking forward to Uniswap v4, we also take this opportunity to take a look at what exciting innovations have appeared in AMMs in the past two years.

iZiSwap's solution

DLAMM model

In May 2022, iZUMi Finance launched iZiSwap, its DEX product, and proposed a brand new AMM model - Discretized-Liquidity-AMM (DLAMM for short).

Mathematical formula used by DLAMM, source: iZiSwap Whitepaper Specifically, DLAMM discretizes the continuous price curve into countless price points based on the constant product model. Except for these points, the transaction price of the trading pair will not have other values during the fluctuation process. Liquidity providers can only provide liquidity at these price points, and traders can only trade at these price points.

Price points in the DLAMM model, source: iZiSwap Whitepaper In DLAMM, the market price will only be at a discrete price point, only the liquidity pool at the market price point contains two types of tokens, the liquidity pool above the market price point contains only one asset, and the liquidity pool below the market price point Price's liquidity pool contains only one other asset. A transaction at any price point will directly affect the change in the proportion of the liquidity pool at that price point, but the transaction price remains unchanged until the liquidity at this price point is traded to only one type, and the market price will move to Adjacent price points and continue to repeat the process.

Advantages of the DLAMM model

After careful observation, it is not difficult to find that the underlying logic of the DLAMM model is actually very similar to the order book model. We believe this is also one of the future development trends of DEX. The introduction of the AMM model by Uniswap was the result of trade-offs in the performance of Ethereum at that time. While providing convenient services for traders, it also brought various problems. With the development and iteration of the infrastructure network, the defects of the AMM model itself will be gradually optimized, and DEX will gradually move closer to the order book model. In November 2022, Trader Joe v2 will be launched, and Trader Joe also uses an AMM model similar to DLAMM in v2.

Compared with the current DEX, the main advantages of the DLAMM model are reflected in the following aspects:

DLAMM and constant product AMM, Source: iZiSwap

• DLAMM's price point is more accurate than the price curve of the constant product model. The price curve of the constant product model is a continuous smooth curve, but the impact of any transaction on the price is not smooth. The constant product model can only determine the price before and after the transaction through the ratio of the liquidity pool before and after the transaction, and the price of each transaction The actual transaction price needs to be calculated according to the changes in the liquidity pool after the actual transaction. For example, when trading on Uniswap, traders need to set the size of the transaction, the maximum slippage that can be tolerated, etc. before trading, and Uniswap will estimate a rough transaction price based on the information submitted by the user. In the case of insufficient liquidity, the estimated price may be far from the actual transaction price. But on iZiSwap, these price points are calculated and determined through discrete price formulas, and p represents the relative price of two tokens in a trading pair. This makes transaction prices more predictable and increases the transparency of transactions.

In DLAMM, the calculation formula for determining the relative price point, source: iZiSwap Whitepaper

• While meeting traders' demand for price accuracy, DLAMM further improves capital utilization efficiency. In real life, when people describe the price of a token, they often do not describe it very precisely, but are used to having a minimum increment interval. For example, when the price of $ETH is $1,817.26, it often only needs to be accurate to the single digit of $1,817, and sometimes even only needs to be accurate to the tens digit of $1,820. Therefore, using a relative minimum price increment interval of 1‱ is, in most cases, sufficient to accommodate traders' sensitivity to prices. At the same time, this design also allows the liquidity in a similar range of price points to gather at the price point, further improving the capital utilization rate. Traders trade within a certain price point conforming to the constant sum model, that is, in the case of sufficient liquidity, transactions within a single price point will not even generate slippage.
• Fully compatible with limit orders. Since DLAMM determines the tradable price points in advance, it is also possible to adapt limit orders. In December 2022, iZiSwap launched a new version of iZiSwap Pro. In this new version, iZiSwap provides an on-chain price limit order. The limit order submitted by the trader will be added to the liquidity pool of the price point in the form of reverse liquidity. When the market price fluctuation falls within the range of the trader's order, this part of the liquidity will be matched with the liquidity provided by LP. Sexual hedging to achieve limit order transactions. Synchronized with the limit order, iZiSwap also launched a user interface adapted to the limit order mode. Users can also switch between the classic AMM DEX trading interface and the limit order trading interface at any time. Whether they are traders who are used to AMM DEX or centralized exchanges, they can smoothly complete transactions on iZiSwap.

iZiSwap Pro limit order mode UI interface, source: iZiSwap

• Compared with the order book DEX currently on the market, the limit order DLAMM is more secure. Because the current order book DEX is still composed of an off-chain transaction matching engine and on-chain transaction records. For example, in order to trade on dYdX, traders need to make a deposit on dYdX first. Although this deposit transaction is recorded on the blockchain, and every transaction of the user on dYdX will be sent back to the Ethereum mainnet in the form of Rollup with zero-knowledge proof. However, DLAMM is still an AMM. Traders only interact with the liquidity pool and do not need a counterparty. Therefore, there is no need for a centralized transaction matching engine. They only need to place an order and wait for the market price to reach the order price before the transaction is completed. On iZiSwap, user interaction does not require deposits and withdrawals, eliminating the risk of fund custody.

Write at the end

Since its launch in May 2022, iZiSwap has gone through a year of development practice, and DLAMM has withstood the test of traders. At the same time, iZiSwap is also constantly updated to provide users with a better trading experience. These user-friendly innovations are indeed seen by users. After the launch of zkSync Era, the TVL of iZiSwap quickly rose to over $100 million.

iZiSwap transaction data, source: iZiSwap We believe that AMM-based innovation will not stand still. When will the era of Uniswap v4 come? Can it bring us a bigger surprise? It's hard to say, but iZiSwap has laid another solid foundation on the road of AMM innovation, making the future of AMM even more worth looking forward to.