Original editor: Biteye core contributor Crush

Original editor: Biteye core contributor Crush

It has been more than a year and a half since Uniswap launched the V3 version, and the concept of "aggregated liquidity" proposed by it has been taken for granted by users. According to the analysis data provided by the Uniswap official website, the TVL of V3 is more than three times that of V2, and the daily trading volume is more than 10 times.

Concentrated liquidity allows users to actively choose the price range in which they provide liquidity, which significantly improves the LP capital efficiency of V3, but it does not change the constant product formula that defines LP, that is to say, impermanent losses still exist, and as funds Efficiency is improved and relatively enlarged;

User transactions still have slippage and are vulnerable to sandwich attacks. From the user's point of view, limit orders are more customary and more beneficial trading methods, but V3 does not do this.

Uniswap V3 actually already has the concept of a price range, and the definition of liquidity in each range is different due to the upper and lower limits of the price range, as follows:

Since LP cannot track market price changes in real time, once the price exceeds the selected range, the LP pair itself will become a single currency liquidity, and there will be losses compared to the existing market price.

Institutional and professional investors obviously have an advantage in tracking market prices; and a recent data analysis pointed out that investors who provide liquidity for Uniswap V3 are in a state of loss as a whole, and the handling fee does not exceed the impermanent loss.

Does AMM really want xy=k to go all the way to black? The author recently noticed a new AMM design idea, and I will share it here.

iZUMi's DL-AMM model

paperpaperproposed in.

This paper is an innovative algorithm proposed for the shortcomings of Uniswap V3, which has the following characteristics:

1. Discretized Contentrated Liquidity

DL-AMM does not use a constant product formula, but places liquidity at discrete different price points, and each price point follows a constant sum formula (x + y = L).

Numerous discrete price points are connected to form a complete AMM price curve similar to Uniswap. At the same time, when placing interval liquidity, DL-AMM uses a new quantitative definition of "liquidity" (L = x*√p + y/√p) to convert the integral summation of Uniswap V3 into an equal ratio summation. Can be done efficiently in constant time.

2. Grouped Limited Liquidity

The liquidity in DL-AMM will be divided into two categories: LP liquidity and limit order liquidity. The former is the same as V3, and the latter is one-way. Once the target price is exceeded, tokens will not be exchanged and reserved Up to the user "claim".

If the liquidity in the group does not completely exceed the target price, "claim" follows the principle of first come, first served. The traditional transaction matching engine needs to train all orders at a price point in rotation. Through innovative algorithm design, DL-AMM can complete the matching in a constant time for the first time, and guarantee the correctness of time, fairness and complete non-custodial funds security.

Compared with Uniswap V3, the DL-AMM proposed by iZUMi avoids transaction slippage at each price point by applying a constant sum formula at different discrete price points, and combines discrete price points (and based on this Liquidity depth) to realize the function of the order book on the chain. The latecomers such as traderjoe's Liquidity Bin are derived from the design of DL-AMM.

Introduction to DL-AMM Model, source: https://izumi.finance/paper/dswap.pdf

The figure shows the constant sum formula used by DL-AMM, different discrete price points correspond to different (p, L), its LP curve (yellow line) and the blue line (constant product formula, xy=k) used by Uniswap The final difference is shown on the left.

It can be seen that if the price range is dense enough, the yellow line can approach the blue line infinitely. At this time, there is no difference between the two in terms of actual trading experience and operating experience.

The picture on the right shows DL-AMM's support for limit orders. The limit order will be used as a special LP (single currency) to provide liquidity together with ordinary LPs, which brings the Limit order function to iZiswap, which Uniswap cannot achieve.

Through these ingenious improvements, DL-AMM has expanded the potential of Uniswap V3 in the limit order function, providing a complete on-chain order book function; and the on-chain order book based on iZiswap DL-AMM can perfectly It avoids the technical difficulties encountered in traditional thinking and provides a new development direction for it.

iZiswap was launched on May 20, 2021, and the product has undergone continuous iterations. The current TVL of the entire chain is about 94.7 M US dollars.

The iZiSwap Pro launched by iZUMi has the on-chain order book function of point-to-pool matching (AMM mode); at the same time, the zero-slip, MEV-proof decentralized limit order is also refreshing.

iZiswap has been launched on multiple chains such as BNB chain/Arbitrum one after another. Since its launch on ZkSync on April 21, in just three weeks, it has become the DEX with the largest TVL on ZkSync.

iZiSwap data on ZkSync

At present, Ref finance on Near and Arctic on Aurora both use iZiswap's original DL-AMM solution. The former is the largest DEX in the Near ecosystem, and its TVL reached 270 million US dollars at its peak.

Trader Joe's Liquidity Book

Traderjoe followed the practice of DL-AMM and set multiple discrete price bins (Liquidity Bin) for LP, and the LP in each price bin is also defined by a constant sum formula (as shown on the left in the figure below).

Liquidity within each price box is provided by multiple users. Taking c as the proportion of token Y in the price box, it is easy to conclude that only the price box c where the current market price is located is between (0, 1).

The price box whose price is higher than the market price is composed of token Y (c= 0 ); the price box whose price is lower than the market price is composed of token X (c= 1 ).

So far, the design of Liquidity Bin is basically the same as DL-AMM, that is, it can also achieve lower slippage.

In itsofficial website, and also provide users with some liquidity adding strategies based on this, so that users can freely match the flow box to realize their own strategy combination.

For example, the "Bid-Ask" strategy in the figure below:

In order to further reduce impermanent losses, Liquidity Bin has designed a transaction rate mechanism associated with price volatility.

Its transaction fee removes the same basic fee part as the traditional mechanism, and also includes a variable fee part (the formula is as follows).

This part of the fee is quadratically related to the volatility accumulator (v_a) (s is the price box length). v_a is used to measure the intensity of price fluctuations. If the price fluctuates too quickly in a short period of time, the variable fee will be increased accordingly to reduce IL through smooth fluctuations and attract liquidity when the fluctuations are too low.

Liquidity Book can be seen as a combination of iZUMi's DL-AMM idea and dynamic rate. Its core is still the replacement of the global constant product formula by the discrete price point constant sum formula, but it currently does not support the Limit Order function.

Since Uniswap came out, xy=k seems to have been the "bible" in the AMM field, because it is simple enough and effective enough.

Due to the lack of the xy=k formula, many teams gradually began to explore new possibilities. The DL-AMM model proposed by iZUMi is just one of them that is practical and beautiful enough.

It can not only support the transaction depth and experience of the original xy=k model, but also bring the reduction of slippage and MEV, as well as new functions such as on-chain order books.

It is believed that there will be more innovations based on DL-AMM in the future to bring more abundant liquidity on the chain, add strategies, and lay a technical foundation for the emergence of new applications (such as user-insensitive on-chain order books).

References

References
[ 1 ] https://Uniswap.org/whitepaper-V3.pdf

[ 2 ] https://docs.izumi.finance/

[ 3 ] https://assets.izumi.finance/paper/dswap.pdf

[ 4 ] https://defillama.com/protocol/ref-finance

[ 5 ] https://help.traderjoexyz.com/en/trader-joe/liquidity-book

[ 6 ] https://github.com/traderjoe-xyz/LB-Whitepaper/