trade prices are. unchanged. xy = k. means that the price is determined based on the constant factor k. (DEX). Liquidity Implication of Constant Product . In non-custodial AMMs, user deposits for trading pairs are pooled within a smart contract that any trader can use for token swap liquidity. After a trade, theres a new spot price, at a different point on the curve. This type of AMM will adjust its exchange rates automatically based on demand and supply to maintain that ratio. how it works. A trader could then swap 500k dollars worth of their own USDC for ETH, which would raise the price of ETH on the AMM. The law of supply and demand tells us that when demand is high (and supply is constant) To build a better intuition of how it works, try making up different scenarios and It sets the trading price between them based on the . The pool also takes a small fee ($r = 1 - \text{swap fee}$) from the amount of token 0 we gave. If there is not enough liquidity (i.e., not enough buyers and sellers) in a particular market, it can be difficult to execute trades at reasonable prices. Instead, there needed to be many ways to trade tokens, since non-AMM exchanges were vital to keeping AMM prices accurate. The above calculations might seem too abstract and dry. This example is from the Desmos chart made by Dan Robinson, If there is a bug in the smart contract, or if it is exploited by malicious actors, it could result in the loss of funds or other problems. Liquidity Pool:a liquidity pool is a collection of assets that is used to facilitate trading in an AMM.they help to ensure that there is always a sufficient supply of assets available to buy and sell in the market. costs 0.001 ETH. We derive the value function for liquidity providers . the constant product function implements this mechanism! And: Since AMMs usually have a fee, the product of the reserves is not really a constant in practice. building one specific type of AMMConstant Function Market Maker. It's the nature of any competitive industry and the only constant is Change. Smart contract risk: As with any decentralized platform, constant product AMM DEXs rely on smart contracts to facilitate trades and manage assets. This can be done by depositing assets into a liquidity pool, which is then used to facilitate trading in the market. [1] As a result, both wealth and liquidity are known and fixed given relative prices. The first and most well-known AMM is the Constant Product Market Maker (CPMM), first released by Bancor in the form of bonding curves within "smart token" contracts, and then further popularized by Uniswap as an invariant function [2][3]. buy a smaller amount. The actual price of the trade is the slope of the line connecting the two points. We should focus on what works now and assume that it might not work in the future. One of the most popular models adopted by automated market maker platforms is the constant product market maker (CPMM) model. based on the input amount and vice versa: $$\Delta y = \frac{yr\Delta x}{x + r\Delta x}$$ The price of tokens in the AMM before adding the liquidity = X/Y. Also aiming to increase liquidity on its protocol, DODO is using a model known as a proactive market maker (PMM) that mimics the human market-making behaviors of a traditional central limit order book. The constant formula is a unique component of AMMs it determines how the different AMMs function. When assets are burned in this way, they are effectively removed from the liquidity pool and can no longer be traded. "Decentralized Finance: On Blockchain- and Smart Contract-Based Financial Markets", "A Practical Liquidity-Sensitive Automated Market Maker", "Logarithmic markets coring rules for modular combinatorial information aggregation", https://github.com/patrick-layden/HyperConomy, https://en.wikipedia.org/w/index.php?title=Constant_function_market_maker&oldid=1141745032, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 26 February 2023, at 15:49. A market maker faces the following demand and supply for widgets. Please try again. Concluding from the law of supply and demand, high demand increases the priceand this is a property we need to have Unlike traditional order book-based exchanges, traders trade against a pool of assets rather than a specific counterparty. If 1 ETH costs 1000 USDC, then 1 USDC This practice ensures that a market maker is readily available to buy or sell an asset themselves should there be no natural buyer or seller. This product remains constant during the token swap process such that for time t+1. of reserves must not change. AMMs use a constant product formula . You need to enable Javascript to view this site properly. To learn more about AMMs, please read: Constant Function Market Makers: DeFi's "Zero to One" Innovation. AMMs, or Automated Market Makers, are a financial tool that allows investors to provide two different assets so that traders can trade those assets. In many markets, there may not be enough organic liquidity to support active trade. Well, this is the math of Uniswap V2, and were studying Uniswap V3. Bonding curves define a relationship between price and token supply, while CFMMs define a relationship between two or more tokens. The main advantage of constant product AMMs is that they are relatively simple to understand and use. I believe that these algorithmic markets utilize a type of AMM that is not a CFMM because the interest rate function is dynamic based on the utilization ratio and the goal is not to keep the interest rate constant. Constant Price Market . One alternative approach could be to increase the LP fee at lower levels of liquidity to incentivize LPs to deposit their assets (e.g. Today, you can farm for yield maximize profits by moving LP tokens in and out of different DeFi apps. In practice, because Uniswap charges a 0.3% trading fee that is added to reserves, each trade actually increases k. A constant product function forms a hyperbola when plotting two assets, which has a desirable property of always having liquidity as prices approach infinity on both sides of the spectrum. On a. , buyers and sellers offer up different prices for an asset. The structure of the paper is as follows. {\displaystyle \varphi } a ETH/USDC pool, ETH is priced in terms of USDC and USDC is priced in terms of ETH. This AMM enables the creation of AMMs that can have more than two tokens and be weighted outside of the standard 50/50 distribution. Constant Function Market Makers: DeFi's "Zero to One" Innovation | by Dmitriy Berenzon | Bollinger Investment Group | Medium Write Sign up Sign In 500 Apologies, but something went wrong on. The essence of current versions of automated market makers is best expressed through the constant product equation: x * y = k. Based on it, if a swap pool owns some units of token x and some units of token y, it prices trades so that the quantities of x and y resulting after the trade, when multiplied, are equal to a fixed constant, k. The protocol uses globally accurate market prices from Chainlink Price Feeds to proactively move the price curve of each asset in response to market changes, increasing the liquidity near the current market price. . As we will see many times in this book, this simple requirement is the core algorithm of how AMMs provide liquidity to the DEX by constantly buying and selling assets in order to keep prices stable. Constant Product Market Maker (CPMM): A type of automated market maker that holds a fixed value for the ratio of two tokens it is trading, also known as a constant product formula. Uniswap popularized the mathematical formula: In this article I explain what Automated Market Makers are, and dive deep into Constant Product Market Makers. and they also take the trade amount ($\Delta x$ in the former and $\Delta y$ in the latter) into consideration. It uses the following functions: Where U(x) could be interpreted as a utility function comprised of a gain function, G(x), and a loss function, F(x); and x is the reserves of each asset. A distributed network for decentralized protocols enabling the most lucrative, fastest and protected operations in DeFi. Interestingly, this brings us back to the initial use-case of AMMs, which was information elicitation, except this time it is about the price of an asset rather than the probability of an event occurring! Instead of matching buyers and sellers in an orderbook, these liquidity pools act as an automated market maker. As a liquidity provider you just need . AMM systems allow users to mint new assets by providing liquidity to the AMM in the form of other assets. A qualified professional should be consulted prior to making financial decisions. In practice, what would happen is that any arbitrageur would always drain one of the reserves if the reference relative price of the reserve tokens is not one. $$r\Delta x = \frac{x \Delta y}{y - \Delta y}$$ Phew! When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. This incentivises and rewards LPs proportionally to their ownership percentage of the pool. However, the execution price is 0.666, so we get only 133.333 of token 1! One simple example of a trading function is the product [Lu17,But17], implemented by Uniswap [ZCP18] and SushiSwap [Sus20]; this CFMM accepts a trade only . Lets visualize the constant product function to better understand While it is true that Uniswap is an AMM, we could refer to it with more specificity. Since Uniswap pools are separate smart contracts, tokens in a pool are priced in terms of each other. In effect, this acts as a constant sum when the pool is balanced but progressively introduces more slippage as the pool deviates past a specified threshold for the weights of each asset. ( Ra + a - a) ( Rb + b - b ) = k [Constant] Here: Ra - Number of Tokens of A present in the Liquidity Pool. $$r\Delta x = \frac{xy - xy + x \Delta y}{y - \Delta y}$$ Proposition: For \(x>x^*\), constant product provides "higher" risk compensation than what market competition would yield, for \(x<x^*\) it is the reverse. The purple line is the curve, the axes are the reserves of a pool (notice that theyre equal at the start price). [5] First be seen in production on a Minecraft server in 2012,[6] CFMMs are a popular DEX architecture. The pool stays in constant balance, where the total value of ETH in the pool will always equal the total value of BTC in the pool. Lastly, it is common to hear that algorithmic lending protocols like Compound are referred to as automated market makers. An interesting area of research would be to analyze the profit-maximizing fee that balances trade incentivization with liquidity incentivization. Rb - Number of Tokens of B present in the Liquidity Pool. Another approach could be to have decreased LP fees at the markets initiation to encourage trading volume and increase the fees as the market matures. Path dependence, in a nutshell, means that history matters. This function acts as a constant sum when the portfolio is balanced and shifts towards a constant product as the portfolio becomes more imbalanced. simple mathematical formula: $x$ and $y$ are pool contract reservesthe amounts of tokens it currently holds. The most popular of them is the Constant Function Market Makers (CFMM) [37], which maintain a mathematical invariant (for example, a product of the quantity of assets) during the trade. Automated market makers (AMMs) are algorithmic agents that perform those functions and, as a result, provide liquidity in electronic markets. $$-\Delta y = \frac{xy}{x + r\Delta x} - y$$ In this situation, AMM liquidity providers have no control over which price points are being offered to traders, leading some people to refer to AMMs as lazy liquidity thats underutilized and poorly provisioned. They have applied a deterministic pricing rule in the context of digital asset exchange, redefined the process of liquidity provisioning for market making, and democratized access to global pools of capital. Conversely, the price of BTC goes down as there is more BTC in the pool. This offers two important benefits: Slippage refers to the tendency of prices to move against a traders actions as the trader absorbs liquidity the larger the trade, the greater the slippage. the larger the liquidity pool, the lower the price slippage) but there are additional dimensions that could be dynamic. [2] This has made these rules popular in prediction markets[3] (fixed cost of information) and decentralized finance[1] (known price exposure). Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. $$r\Delta x = \frac{xy - x(y - \Delta y)}{y - \Delta y}$$ means there is a constant balance of assets that determines the price of tokens in a liquidity pool. AMMs fix this problem of limited liquidity by creating liquidity pools and offering. Lets return to the trade formula and look at it closer: As you can see, we can derive $\Delta x$ and $\Delta y$ from it, which means we can calculate the output amount of a trade of the first token and y is the reserve of the other token, and the order doesnt matter. in a permissionless system. . An automated market maker is a type of decentralized exchange that lets customers trade between on-chain assets like USDC and ETH. Constant product formula is probably the simplest and the earliest algorithm to come into the market. The relationship. And its the slope of the tangent line at This design ensures that the pool remains balanced according to its pre-set weights for each asset. A constant-function market maker (CFMM) is a market maker with the property that the amount of any asset held in its inventory is completely described by a well-defined function of the amounts of the other assets in its inventory. The more assets in a pool and the more liquidity the pool has, the easier trading becomes on decentralized exchanges. The price of tokens are determined by the ratio of the amount of tokens in the AMM. Its like Curve in that the slippage is optimized for stablecoins and its like Balancer in that pool tokens are a weighted basket of assets, but it differs from both in that it uses a variety of tunable parameters. Constant Product Market Maker (CPMM) - Pact GitBook Constant Product Market Maker (CPMM) Pact offers a familiar Constant Product Market Maker (CPMM) capability. Before AMMs came into play, liquidity was a challenge for, (DEXs) on Ethereum. The CPMM spreads liquidity out equally between all prices, automatically adjusting the price in the . Saint Fame further legitimized the concept by selling shirts, Zora generalized the concept by creating a marketplace for limited-edition goods, and I expect to see many more projects using CFMMs for this use-case. This design unfortunately allows arbitrageurs to drain one of the reserves if the off-chain reference price between the tokens is not 1:1. This relationship between the prices of asset A and asset B is known as "constant product price elasticity." In the real world, everything is priced based on the law of supply and demand. Recorded talk for the paper Improved Price Oracles: Constant Function Market Makers by Guillermo Angeris and Tarun Chitra for ACM's Advances in Financial Tec. Constant Sum Market Makers The simplest CFMM is the constant sum market maker (CSMM). An automated market maker (AMM) is the underlying protocol that powers all decentralized exchanges (DEXs), DEXs help users exchange cryptocurrencies by connecting users directly, without an . Previous Multiple Fee Tiers Next StableSwap Invariant Market Maker (SIMM) Last modified 3mo ago V How do we calculate the prices of tokens in a pool? $$-\Delta y = \frac{xy - xy - y r \Delta x}{x + r\Delta x}$$ At its core, a liquidity pool is a shared pot of tokens. . [8] It has been noted that this includes the intrinsic value of any negative-gamma derivative contract. This mechanism ensures that Pact prices always trend toward the market price. Because CFMMs encourage passive market participants to lend their assets to pools, they make liquidity provisioning an order-of-magnitude easier. And we dont even need to calculate the prices! If (AMMs) allow digital assets to be traded without permission and automatically by using, instead of a traditional market of buyers and sellers. 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