StableSwap is primarily designed for trading stablecoins (coins pegged to a fiat currency), and has a different slippage profile compared to either of its predecessors. Adding liquidity to a CFMM is simple but comes with some complex financial risks (impermanent loss, short volatility, long volatility/volume correlation, etc.). [5] First be seen in production on a Minecraft server in 2012,[6] CFMMs are a popular DEX architecture. Were basically giving a pool some amount of token 0 and getting some amount of token 1. For example, the Uniswap payoff curve is concave, meaning that liquidity providers are profitable within a certain price bound and will lose money in large price movements: Ideally, we want convexity when taking risk, which means having upside on both sides of the risk spectrum. When we buy token 1 for token 0, we give some amount of token 0 to the pool ($\Delta x$). $12 b. ; Tarun Chitra, Guillermo Angeris, Alex Evans, and Hsien-Tang Kao. Adding a bid-ask spread on top of a CFMM breaks the constant-function invariant. The law of supply and demand tells us that when demand is high (and supply is constant) The most commonly used AMM is constant product AMM, but other AMM models are also deployed in decentralized finance (DeFi). And when demand is low, the price is also lower. $$\Delta y = \frac{y r \Delta x}{x + r\Delta x}$$ The formula is: When you trade in an AMM X and Y can vary but the result is always a constant. Were selling 200 of token 0. Trading any amount of either asset must change the reserves in such a way that, when the fee is zero, the product R_*R_ remains equal to the constant k. This is often simplified in the form of x*y=k, where x and y are the reserves of each asset. For example: in We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). Every trade starts at the point on the curve that corresponds to the current ratio of Typically, the exchange has to find market makers, have them write custom code for pricing and posting orders, and often directly provide accounts and funds on which to trade. Constant Price Market . Well put the demand part aside for now and focus on supply. In this paper, we focus on the analysis of a very large class of automated market makers, called constant function market makers (or CFMMs) which includes existing popular market makers such as Uniswap, Balancer, and Curve, whose yearly transaction volume totals to billions of dollars. More detailed . Constant Function Market Makers This chapter retells the whitepaper of Uniswap V2. Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. AMMs democratized cryptocurrency trading by doing away with order books and institutional market makers. The job of the pool is to give 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. Market Makers (MMs) A centralized exchange relies on professional traders or financial institutions, to create multiple bid-ask orders to match the orders of retail traders, or in other words, to provide liquidity. As a new technology with a complicated interface, the number of buyers and sellers was small, which meant it was difficult to find enough people willing to trade on a regular basis. Uniswap V2 / constant-product AMM implemented in Solana's Anchor -- add and remove liquidity, swap tokens, earn fees! To calculate the output amount, we need to find a new point on the curve, which has the $x$ coordinate of $x+\Delta x$, i.e. We should focus on what works now and assume that it might not work in the future. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. 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. [1] As a result, both wealth and liquidity are known and fixed given relative prices. How does the Constant Product Market Maker (CPMM) work? In effect, the function looks like a zoomed-in hyperbola. Product-market fit is a moving target. based on the input amount and vice versa: $$\Delta y = \frac{yr\Delta x}{x + r\Delta x}$$ Perpetual Protocol's vAMM uses the same x*y=k constant product formula as Uniswap. After a trade, theres a new spot price, at a different point on the curve. Ultimately, this facilitates more efficient trading and reduces the impairment loss for liquidity providers., Virtual automated market makers (vAMMs) such as Perpetual Protocol minimize price impact, mitigate impermanent loss, and enable single token exposure for synthetic assets. and states that trades must not change the product (. Anyone with an internet connection and in possession of any type of ERC-20 tokens can become a liquidity provider by supplying tokens to an AMMs liquidity pool. 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. Therefore, they are the "source" of price discovery for trades. They allow digital assets to be traded in a permissionless and automatic way by using liquidity pools rather than a traditional market of buyers and sellers. The third type is a constant mean market maker (CMMM), which enables the creation of AMMs that can have more than two tokens and be weighted outside of the standard 50/50 distribution. to the pool, which is added to the reserves. 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. Francesco in Coinmonks For a large part of the history of finance, market making activity was carried out by institutions with large capital and resources. Copyright 2023 Gemini Trust Company, LLC. This fee is paid by traders who interact with the liquidity pool. Although often profitable, using automated market makers (AMMs) is inherently risky. Traditional AMM designs require large amounts of liquidity to achieve the same level of price impact as an order book-based exchange. By trading synthetic assets rather than the underlying asset, users can gain exposure to the price movements of a wide variety of crypto assets in a highly efficient manner. Lets visualize the constant product function to better understand By tweaking the formula, liquidity pools can be optimized for different purposes. put some amount of one token into a pool (the token they want to sell) and remove some amount of the other token from the pool in a permissionless system. 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. The constant product market maker protocol is a form of the much known automated market maker (AMM) model. This payoff structure suggests that liquidity providers should be actively monitoring changes in the liquidity pool and acting on changes quickly to prevent significant losses. Visually, the prices of tokens in an AMM pool follow a curve determined by the formula. The above calculations might seem too abstract and dry. As the "virtual . The reserve of token 0 changes ($x + r \Delta x$), and the reserve of token 1 changes as well ($y - \Delta y$). and this is a desirable property! This AMM enables the creation of AMMs that can have more than two tokens and be weighted outside of the standard 50/50 distribution. Curve and Shell have demonstrated that there exists a design space for constant functions that are tailored for specific types of digital assets. Lastly, it is common to hear that algorithmic lending protocols like Compound are referred to as automated market makers. Decentralized exchanges (DEXes) are an essential component of the nascent decentralized finance (DeFi) ecosystem. the incentive to supply these pools with assets. Constant product automated market makers (CPMM): These market makers use a fixed product formula to ensure that the value of a particular market remains constant. For example, if an AMM has ether (ETH) and bitcoin (BTC), two volatile assets, every time ETH is bought, the price of ETH goes up as there is less ETH in the pool than before the purchase. Liquidity implications of constant product market makers. They do this by using a process called "liquidity provision," in which they act as both the buyer and the seller of an asset. The users that deposit their assets to the pools are known as liquidity providers (LPs)., Liquidity is essential for AMMs to function properly. Eleven sellers are also willing to sell at the same prices. Liquidity providers normally earn a fee for providing tokens to the 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. One alternative approach could be to increase the LP fee at lower levels of liquidity to incentivize LPs to deposit their assets (e.g. 2021. Liquidity Implication of Constant Product . On a traditional exchange platform, buyers and sellers offer up different prices for an asset. In the real world, everything is priced based on the law of supply and demand. The first AMM were developed by Shearson Lehman Brothers and ATD. The information provided on the Site is for informational purposes only, and it does not constitute an endorsement of any of the products and services discussed or investment, financial, or trading advice. 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. arXiv preprint arXiv:2103.01193, 2021. 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. Because of this, CSMM is a model rarely used by AMMs. This changes the reserves of the pool, and the constant function formula says that the product 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 ? real estate). This also holds true for AMMs. Today, you can farm for yield maximize profits by moving LP tokens in and out of different DeFi apps. Curve offers low-price-impact swaps between tokens that have a relatively stable 1:1 exchange rate. Understanding this math is crucial to build a Uniswap-like DEX, but it's totally fine if you don't understand everything at this stage. Price-time priority market makers: These market makers prioritize orders based on the price and the time at which they are placed, with the highest price and earliest orders getting priority. 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. Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. Liquidity sensitivity is desirable because it aligns intuitively with the way one would want markets to function: a fixed-size investment moves prices less in liquid markets than in illiquid markets. V 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. 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. Available at SSRN 3808755, 2021. Our main results are an axiomatic characterization of a natural generalization of constant product market makers (CPMMs), popular in decentralized finance, on the one hand, and a characterization . Something went wrong while submitting the form. This leads us to the following conclusion: pools decide what The portfolio value is concave in the relative price of pool assets, short volatility, and can be effectively hedged in the same manner as a vanilla option. Instead of matching buyers and sellers in an orderbook, these liquidity pools act as an automated market maker. 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]. Automated market makers (AMMs) are a type of decentralized exchange (DEX) that use algorithmic money robots to make it easy for individual traders to buy and sell crypto assets. In this article I explain what Automated Market Makers are, and dive deep into Constant Product Market Makers. of Uniswap V3 is different. a - Number of Tokens of A the trader has . When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. This example is from the Desmos chart made by Dan Robinson, An automated market maker facilitates trades and allows digital assets to be traded on a decentralized exchange (DEX). 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. Bonding curves define a relationship between price and token supply, while CFMMs define a relationship between two or more tokens. However, the execution price is 0.666, so we get only 133.333 of token 1! means there is a constant balance of assets that determines the price of tokens in a liquidity pool. Well, this is the math of Uniswap V2, and were studying Uniswap V3. The opinions and views expressed in any Cryptopedia article are solely those of the author(s) and do not reflect the opinions of Gemini or its management. The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. Market makers do this by buying and selling assets from their own accounts with the goal of making a profit, often from the spreadthe gap between the highest buy offer and lowest sell offer. However, users holding an open position in a synthetic asset are at risk of having their collateral liquidated if the price moves against them.. CSMMs follow the formula x+y=k, which creates a straight line when plotted. This implies a price of 1 ETH = 100 DAI. 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. tokens that the pool is holding. prediction markets). While most people think of Uniswap when they think of AMMs, the concept has actually been studied extensively in academic literature for over a decade, the majority of which were primarily designed for information aggregation and implemented in markets where payoffs depend on some future state of the world (e.g. Notice that each of these formulas is a relation of reserves ($x/y$ or $y/x$) So in the next part, well see how the mathematics However, AMMs have a different approach to trading assets. 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