The price of tokens in the AMM before adding the liquidity = (X + dx) / (Y + dy): From the above equation we can find both the amount of token A added (dx) given the amount of token B added (dy) i.e what is dy given dx ? The same is true for any other pool, whether its a stablecoin pair or not (e.g. 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. 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. This implies a price of 1 ETH = 100 DAI. These With the Constant Product Market Maker (CPMM) capability, pairs act as automated market makers, ready to accept one token for the other as long as the constant product formula is preserved. For example, Curve AMMsknown as the stableswap invariantcombine both a CPMM and CSMM using an advanced formula to create denser pockets of liquidity that bring down price impact within a given range of trades. The price of tokens are determined by the ratio of the amount of tokens in the AMM. If we increase liquidity by 5% the shares also increase by 5 %. A constant sum function forms a straight line when plotting two assets, resulting in the equation x+y=k. V The opposite happens to the price of BTC in an ETH-BTC pool. Liquidity providers normally earn a fee for providing tokens to the pool. Constant Product Formula Automated Market Maker Variations Automated market makers (AMMs) allow digital assets to be traded without permission and automatically by using liquidity pools instead of a traditional market of buyers and sellers. Suggested . 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! 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. An automated market maker is a type of decentralized exchange that lets customers trade between on-chain assets like USDC and ETH. Delta neutral market makers also have a difficult task at hand if they have to find a way to hedge assets off their books since it is often not possible if a natural buyer or seller does not exist. The main advantage of constant product AMMs is that they are relatively simple to understand and use. To create a new Constant Product AMM (CPAMM) between two assets X and Y, a user, called a liquidity provider, or LP, deposits reserves x and y of those two assets. This also holds true for AMMs. When expanded it provides a list of search options that will switch the search inputs to match the current selection. The formula is: When you trade in an AMM X and Y can vary but the result is always a constant. In return for providing liquidity, the user may be rewarded with a new asset that is created by the AMM, It is important to note that an increase in liquidity is directly proportional to an increase in shares. The actual price of the trade is the slope of the line connecting the two points. arxiv: 1911.03380 [q-fin.TR] Google Scholar; Jun Aoyagi and Yuki Ito. Market makers like Citadel can be found in all types of markets from equity to currency exchanges to forex markets and are regarded as an important part of a well functioning and liquid market. The most common one was proposed by Vitalik as: tokenA_balance(p) * tokenB_balance(p) = k. The constant, represented by k means there is a constant balance of assets that determines the price of tokens in a liquidity pool. The pool gives us some amount of token 1 in exchange ($\Delta y$). a ETH/USDC pool, ETH is priced in terms of USDC and USDC is priced in terms of ETH. The term constant function refers to the fact that any trade must change the reserves in such a way that the product of those reserves remains unchanged (i.e. AMMs use a constant product formula . Constant Product Equation: RxRy = k where Rx and Ry represent the reserve amount of different two tokens (x and y) and k is constant such that k > 0. As such, most liquidity will never be used by rational traders due to the extreme price impact experienced. As such, I believe that we will have a variety of CFMMs designed for asset types in addition to stablecoins, such as derivatives (e.g. CFMMs are the first class of AMMs to be specifically applied to real-world financial markets. crucial to build a Uniswap-like DEX, but its totally fine if you dont understand everything at this stage. prediction markets). We use x and y to refer to reserves of one pool, where x is the reserve However, the execution price is 0.666, so we get only 133.333 of token 1! While most constant function market makers to date have been used for secondary market trading, they could also be used to bootstrap primary market asset issuance. Available at SSRN 3808755, 2021. Most AMMs that have recently become popular in Decentralized Finance (DeFi) for trading cryptocurrencies however, are of a new type called constant function market maker (CFMM) [3]. $12 b. On this Wikipedia the language links are at the top of the page across from the article title. Conversely, the price of BTC goes down as there is more BTC in the pool. Since AMMs dont automatically adjust their exchange rates, they require an arbitrageur to buy the underpriced assets or sell the overpriced assets until the prices offered by the AMM match the market-wide price of external markets. Under this option, liquidity providers need to supply each token in the pair with an equal or 50:50 value. Exchanges often have to handle some of the execution themselves by running an internal trading desk with controls to make sure theyre not front-running their customers. On a. , buyers and sellers offer up different prices for an asset. This changes the reserves of the pool, and the constant function formula says that the product A qualified professional should be consulted prior to making financial decisions. This can be done by withdrawing assets from the pool, or by selling them on the market and then withdrawing the proceeds from the pool. The purple line is the curve, the axes are the reserves of a pool (notice that theyre equal at the start price). 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]. However, the actual price of a trade While other types of decentralized exchange (DEX) designs exist, AMM-based DEXs have become extremely popular, providing deep liquidity for a wide range of digital tokens., Underpinning AMMs are liquidity pools, a crowdsourced collection of crypto assets that the AMM uses to trade with people buying or selling one of these assets. Well, this is the math of Uniswap V2, and were studying Uniswap V3. In non-custodial AMMs, user deposits for trading pairs are pooled within a smart contract that any trader can use for token swap liquidity. When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. This is due to the fact that a substantial portion of AMM liquidity is available only when the pricing curve begins to turn exponential. To build a better intuition of how it works, try making up different scenarios and . 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. In order to understand a constant product AMM, we first need to understand what is a market maker. 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. Stocks, gold, real estate, and most other assets rely on this traditional market structure for trading. Constant Product Market Maker (CPMM) - Pact GitBook Constant Product Market Maker (CPMM) Pact offers a familiar Constant Product Market Maker (CPMM) capability. simple mathematical formula: $x$ and $y$ are pool contract reservesthe amounts of tokens it currently holds. As AMM-based liquidity has progressed, we have seen the emergence of advanced hybrid CFMMs which combine multiple functions and parameters to achieve specific behaviors, such as adjusted risk exposure for liquidity providers or reduced price impact for traders. If 1 ETH costs 1000 USDC, then 1 USDC Adding a bid-ask spread on top of a CFMM breaks the constant-function invariant. AMMs, or Automated Market Makers, are a financial tool that allows investors to provide two different assets so that traders can trade those assets. is calculated differently. vAMMs use the same x*y=k constant product formula as CPMMs, but instead of relying on a liquidity pool, traders deposit collateral to a smart contract. There are a variety of other approaches to AMMs for information aggregation, such as Bayesian market makers (often good for binary markets) and dynamic pari-mutuel market makers (often used for horse racing). You need to enable Javascript to view this site properly. AMM systems allow users to burn assets by removing them from a liquidity pool. 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. It occurs when the price ratio of the tokens they have deposited in a liquidity pool changes after they have deposited the tokens in the pool. The paper also looks at the impact of introducing concentrated liquidity in an AMM. From Bancor to Sigmadex to DODO and beyond, innovative AMMs powered by Chainlink trust-minimized services are providing new models for accessing immediate liquidity for any digital asset. What Are Automated Market Makers (AMMs)? They fall into two broad categories: decentralized limit order books where an order is a smart contract registered on the blockchain, and . We focus particularly on separability and on different invariance properties under scaling. Front Running: This is the procees in which traders try to take advantage of the AMM Formula, for instance if a trader knows that the price of asset A is going to increase, they might try to buy a large amount of asset B before the price starts to decrease. 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. This example is from the Desmos chart made by Dan Robinson, The formula is easy to remember, and users can easily see how changes in the price of one asset will affect the price of the other asset. means there is a constant balance of assets that determines the price of tokens in a liquidity pool. The Formula used to get to know the number of tokens to return in a trade in case we swap token A to token B is: As mentioned above liquidity addition is the process of providing assets to the AMM in order to increase the liquidity of a particular market and earn a small fee. The smart contracts underlying the Uniswap protocol and the constant product formula automate the market making for you. Liquidity Implication of Constant Product . In other words, in the absence of fees, constant mean markets ensure that the weighted geometric mean of the reserves remains constant. Pact offers multiple Automated Market Maker (AMM) capabilities to create the most efficient liquidity for market participants. When we add liquidity it is important to note that there should be no price change before and after adding liquidity. Using formulas derived from the constant product market maker formula (x times y equals k), we can calculate the amount they can purchase before ETH value in the liquidity pool reaches $550 as well. Many of first-generation AMMs are limited by impermanent loss and low capital efficiency, which impacts both liquidity providers and traders. The constant function formula says: after each trade, k must remain unchanged. Uniswap V2 / constant-product AMM implemented in Solana's Anchor -- add and remove liquidity, swap tokens, earn fees! Because of this matching process, there is the possibility that some orders may take a while to get filled, if ever. Eleven buyers are willing to buy at the following prices: $15, $14, $13, $12, $11, $10, $9, $8, $7, $6, $5. Understanding this math is the incentive to supply these pools with assets. Automated market makers (AMMs) are part of the decentralized finance (DeFi) ecosystem. In fact, the creator of the term stated that bonding curve was actually intended to be used in the context of a bonded together curation community. Theres a pool with some amount of token 0 ($x$) and some amount of token 1 ($y$). The change in $y$ is the amount of token 1 well get. value doesnt matter. Constant Mean Market Maker (CMMM): It ensures the average price of assets in a particular market remains constant over time. Path dependence, in a nutshell, means that history matters. Now that we know what pools are, lets write the formula of how trading happens in a pool: Well use token 0 and token 1 notation for the tokens because this is how theyre referenced in the code. Such a situation would destroy one side of the liquidity pool, leaving all of the liquidity residing in just one of the assets and therefore leaving no more liquidity for traders. arXiv preprint arXiv:2103.01193, 2021. The name 'constant product market' comes from the fact that, when the fee is zero (i.e., = 1), any trade to must change the reserves in such a way that the product R R reserves. . $$r\Delta x = \frac{x \Delta y}{y - \Delta y}$$ In a traditional exchange workflow, market makers need to create orders, orders need to be published on exchanges, market takers need to browse orders, and market makers need to wait for the orders to get filled. unchanged. Learn how smart contracts work, use cases, and more. However, users holding an open position in a synthetic asset are at risk of having their collateral liquidated if the price moves against them.. prices when making a trade: And thats the whole math of Uniswap! Users may contribute their assets to the CFMM's inventory, and receive in exchange a pro rata share of the inventory, claimable at any point for the assets in the inventory at that time the claim is made.[1]. In this constant state of balance, buying one ETH brings the price of ETH up slightly along the curve, and selling one ETH brings the price of ETH down slightly along the curve. Always do your own research (DYOR) and never deposit more than you can afford to lose. 0.5% fee below a certain liquidity threshold, 0.3% thereafter). For example, a liquidity pool could hold ten million dollars of ETH and ten million dollars of USDC. money markets, he emphasized that AMMs should not be the only available option for decentralized trading. (DEX). collateralized options) and security tokens (e.g. The product k would actually be constant, if the swap fee was 0%. 2021. The constant product market maker protocol is a form of the much known automated market maker (AMM) model. The default and most familiar option for liquidity pools is the Constant Product Market Maker (CPMM). So, if the price of token A increases, the price of token B must decrease in order to keep the constant product equal to the constant. To incentivize liquidity providers to deposit their crypto assets to the protocol, AMMs reward them with a fraction of the fees generated on the AMM, usually distributed as LP tokens. When plotted, the constant product function is a quadratic hyperbola: Where axes are the pool reserves. And this is where we need to bring the demand part back. It sets the trading price between them based on the . We derive the value function for liquidity providers . Stableswap) had the insight that if the underlying assets are relatively stable-priced (e.g. Please visit our Cryptopedia Site Policy to learn more. in a permissionless system. "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. That there should be no price change before and after Adding liquidity time! There is a constant balance of assets in a liquidity pool constant if. Math of Uniswap V2, and were studying Uniswap V3 goes down as is..., which impacts both liquidity providers and traders CPMM ) this site properly such, most liquidity will never used... 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