The constant product market maker protocol is a form of the much known automated market maker (AMM) model. Copyright 2023 Gemini Trust Company, LLC. $$(x + r\Delta x)(y - \Delta y) = xy$$ This example is from the Desmos chart made by Dan Robinson, On a. , buyers and sellers offer up different prices for an asset. 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. Well be focusing on and In effect, the function looks like a zoomed-in hyperbola. 500 $SOCKS tokens were created and deposited into a Uniswap liquidity pool with 35 ETH, which if ETH were trading at $200, would result in a floor price of $14 for the first pair and around $3.5M for the 499th pair. 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. If we use only the start price, we expect to get 200 of token 1. Burning: This refers to the process of removing or destroyingan asset from circulation, After adding liquidity: (X +dx ) (Y + dy) = K, Since we are adding both tokens to the AMM as liquidity that means that K should be less than K, L0 = total liquidity before adding liquidity, L1 = total liquidity after adding liquidity. 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. Product-market fit is a moving target. 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. 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. To build a better intuition of how it works, try making up different scenarios and In other words, in the absence of fees, constant mean markets ensure that the weighted geometric mean of the reserves remains constant. A qualified professional should be consulted prior to making financial decisions. [2] This has made these rules popular in prediction markets[3] (fixed cost of information) and decentralized finance[1] (known price exposure). On this Wikipedia the language links are at the top of the page across from the article title. If 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. Instead, there needed to be many ways to trade tokens, since non-AMM exchanges were vital to keeping AMM prices accurate. 2019. An analysis of Uniswap markets. we want to buy a known amount of tokens). What Are Automated Market Makers (AMMs)? Excessive Trading? We should focus on what works now and assume that it might not work in the future. Simple question: does it pay to split an order? Eleven sellers are also willing to sell at the same prices. The law of supply and demand tells us that when demand is high (and supply is constant) This new method of exchanging assets embodies the ideals of Ethereum, crypto, and blockchain technology in general: no one entity controls the system, and anyone can build new solutions and participate. Chainlink Price Feeds already underpin much of the DeFi economy and play a key role in helping AMMs accurately set asset prices and increase the liquidity available to traders. Instead of trading directly with other people as with a traditional order book, users trade directly through the AMM.. This has made these rules popular in prediction markets (fixed cost of . This was pioneered by Unisocks, which created tokens that entitled holders to a physical pair of limited edition socks. [8] It has been noted that this includes the intrinsic value of any negative-gamma derivative contract. This allows for variable exposure to different assets in the pool and enables swaps between any of the pools assets. We focus particularly on separability and on different invariance properties under scaling. Smart contract risk: As with any decentralized platform, constant product AMM DEXs rely on smart contracts to facilitate trades and manage assets. You just issued a new stablecoin, X, that is pegged to 1 USDT . This chapter retells the whitepaper of Uniswap V2. While automated market makers have been studied in both theory and practice, constant function market makers (CFMMs) are a zero to one innovation for both academic literature and financial markets. $21. 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. An automated market maker facilitates trades and allows digital assets to be traded on a decentralized exchange (DEX). Please try again. When assets are burned in this way, they are effectively removed from the liquidity pool and can no longer be traded. Because the relative price of the two pair assets can only be changed through trading, divergences between the Pact price and external market prices create arbitrage opportunities. A constant sum function forms a straight line when plotting two assets, resulting in the equation x+y=k. Batch Exchanges with Constant Function Market Makers: Axioms, Equilibria, and Computation Geoffrey Ramseyer, Mohak Goyal, Ashish Goel, David Mazires Economics ArXiv 2022 Batch trading systems and constant function market makers (CFMMs) are two distinct market design innovations that have recently come to Expand 3 PDF Traditional AMM designs require large amounts of liquidity to achieve the same level of price impact as an order book-based exchange. 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. (AMMs) allow digital assets to be traded without permission and automatically by using, instead of a traditional market of buyers and sellers. V The constant product formula . Basically, automated market makers are smart contracts that hold liquidity pools. Concluding from the law of supply and demand, high demand increases the priceand this is a property we need to have The product k would actually be constant, if the swap fee was 0%. 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. In contrast to regular market makers, AMMs function by using self-executing computer programs, also known as smart contracts. Constant Product Market Makers. 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. Liquidity pools can be optimized for different purposes, and are proving to be an important instrument in the DeFi ecosystem. Although Automated Market Makers harness a new technology, iterations of it have already proven an essential financial instrument in the fast-evolving DeFi ecosystem and a sign of a maturing industry. to the pool, which is added to the reserves. Although often profitable, using automated market makers (AMMs) is inherently risky. This property implies that market makers should adjust the elasticity of their pricing response based on the volume of activity in the market. Phew! 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. This can be helpful for traders who want to make informed decisions about which assets to buy or sell. 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. trade prices are. The converse result was later proven, providing a mechanism for constructing a . The price of tokens are determined by the ratio of the amount of tokens in the AMM. Automated market makers (AMM) are decentralized exchanges that pool liquidity from users and price the assets within the pool using algorithms. Only when new liquidity providers join in will the pool expand in size. and states that trades must not change the product (. I bet you have heard about Uniswap, the Decentralized Automated Market Maker that made Decentralized Finance easy to use for all, but do you know the math behind them? Automated market makers (AMMs) are decentralized exchanges that use algorithmic money robots to provide liquidity for traders buying and selling crypto assets. $$r\Delta x = \frac{xy - x(y - \Delta y)}{y - \Delta y}$$ When expanded it provides a list of search options that will switch the search inputs to match the current selection. As the legend goes, Uniswap was invented in Desmos. $$(x + r\Delta x)(y - \Delta y) = xy$$ means there is a constant balance of assets that determines the price of tokens in a liquidity pool. Constant Product Automated Market Maker | Solidity 0.8 - YouTube Code for constant product automated market maker.0:00 - State variables and constructor2:38: Internal functions -. 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. Impermanent Loss is the potential for a market maker to experience a loss due to changes in the relative prices of the assets that they are holding as part of their market making activities. From this, it is observed that when a user places an order of tokens Constant product formula is probably the simplest and the earliest algorithm to come into the market. of Uniswap V3 is different. are the pricing functions that respect both supply and demand. pool reserves. 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. Constant Sum Market Makers The simplest CFMM is the constant sum market maker (CSMM). ; Guillermo Angeris, Alex Evans, and Tarun Chitra. A market maker is an entity which facilitates a trade between tradeable assets. real estate). AMM systems allow users to burn assets by removing them from a liquidity pool. Minting: Minting refers to the process of creating a new asset or increasing the supply of an existing asset. 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. 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. The equation x * y = k governs asset swaps on Uniswap, where x and y represent the quantities of two different assets in a liquidity pool, and k represents a value called the constant product invariant . 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. 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. Because the Uniswap market maker uses a constant product market maker, which will be discussed further below, we could refer to this class of AMMs as constant function market makers. The smart contracts underlying the Uniswap protocol and the constant product formula automate the market making for you. current reserve of token 0 + the amount were selling. Uniswap V2 / constant-product AMM implemented in Solana's Anchor -- add and remove liquidity, swap tokens, earn fees! A Constant Function Market Maker is a class of AMMs where the reserves of the assets in the pool can only change in a way that satisfies a certain mathematical relationship. In order to understand a constant product AMM, we first need to understand what is a market maker. In Vitalik Buterins original post calling for automated or on-chain money markets, he emphasized that AMMs should not be the only available option for decentralized trading. Conversely, the price of BTC goes down as there is more BTC in the pool. Were basically giving a pool some amount of token 0 and getting some amount of token 1. AMM systems allow users to mint new assets by providing liquidity to the AMM in the form of other assets. Constant function market makers (CFMMs), such as constant product market makers, constant sum market makers, and constant mean market makers, are a class of first-generation AMMs made popular by protocols like Bancor, Curve, and Uniswap. 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. And its the slope of the tangent line at 0.3% regardless of the size of the liquidity pool). Market makers are agents that alleviate this problem by facilitating trade that would otherwise not occur in those markets. 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. Such a simple formula guarantees such a powerful mechanism! Only when new liquidity providers join in will the pool expand in size. Answers: a. 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. Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. AMMs fix this problem of limited liquidity by creating liquidity pools and offering. Users trade against the smart contract (pooled assets) as opposed to directly with a counterparty as in order book exchanges. must be monotone (intermediate value theorem), and it can be assumed WLOG that (the token they want to buy). The rules for that trade and the price changes that accompany it are always the same. While there has been a lot of excitement in the crypto community around automated market makers, there has been a lot of confusion over terminology. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged. The above calculations might seem too abstract and dry. Curvature and market making. 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. arxiv: 2012.08040 [q-fin.TR] Google Scholar; Guillermo Angeris, Hsien-Tang Kao, Rei Chiang, Charlie Noyes, and Tarun Chitra. Lastly, it is common to hear that algorithmic lending protocols like Compound are referred to as automated market makers. Shell Protocol has similar goals but takes a different approach. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged: Uniswap, Curve, and Balancer. In non-custodial AMMs, user deposits for trading pairs are pooled within a smart contract that any trader can use for token swap liquidity. Why there are only two reserves, x and y?Each Uniswap pool can hold only two tokens. AMMs are a financial tool unique to Ethereum and decentralized finance (DeFi). 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. 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 ($\Delta x$). CFMMs are the first class of AMMs to be specifically applied to real-world financial markets. We can always find the output amount using the $\Delta y$ formula In an AMM, when adding liquidity to a pool,we must always add a pair of assets(two tokens). . Liquidity Implication of Constant Product . Since Bancor introduced on-chain AMMs in 2017, there have been several notable improvements on different aspects of AMMs: . in a permissionless system. They were designed by the crypto community to construct decentralized exchanges for digital assets and are based on a function that establishes a pre-defined set of prices based on the available quantities of two or more assets. Previous Multiple Fee Tiers Next StableSwap Invariant Market Maker (SIMM) Last modified 3mo ago Conversely, the price of BTC goes down as there is more BTC in the pool. 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. 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. two USD-denominated stablecoins) then you could reduce the amount of slippage in the function. 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. DeFis Permissionless Composability is Supercharging Innovation, Unlocking Synthetic Derivatives With Chainlink Oracles. of reserves must not change. 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. Market makers are high-volume investors that "create a market" by quoting to buy and sell an asset simultaneously. k is just their product, actual Constant Product Market Makers A constant product market maker, first implemented by Uniswap satisfies the equation: where x > 0 and y > 0 are reserves of assets X and Y respectively and k is a constant. A constant mean market maker is a generalization of a constant product market maker, allowing for more than two assets and weights outside of 50/50. Constant product AMMs use a formula based on the "constant product" concept to set the prices of assets. In Vitalik Buterins original post calling for automated or. Professional market makers who ensure that exchanges have enough liquidity, need to be able to rapidly cancel and update their orders when market prices move (which they always do!). You need to enable Javascript to view this site properly. 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. Try different reserves, see how output amount changes when $\Delta x$ is small relative to $x$. Understanding this math is Under this option, liquidity providers need to supply each token in the pair with an equal or 50:50 value. Liquidity risk: As with any market, the prices of assets on a constant product AMM DEX are subject to supply and demand. 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. 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. 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. Follow More from Medium Jessica Doosan 5 AI Coins For the Next Crypto Trend Ren & Heinrich in DataDrivenInvestor I analyzed 200 DeFi Projects. Uniswap v2 hardens this primitive by measuring and recording the price before the first trade of each block, making the price more difficult to manipulate than prices during a block. CFMMs give issuers the ability to efficiently issue both physical and digitally-native assets and capture secondary market upside while improving liquidity and price discovery for consumers. Like most AMMs, Uniswap facilitates trading between a particular pair of assets by holding reserves of both assets. 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! Liquidity refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. Uniswap went live in November 2018 and epitomized the first automated market maker in the ethereum ecosystem, a model that then became ubiquitous and sparked a number of Uniswap clones (SushiSwap, PankakeSwap, MoonSwap). 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 The most common DEXes are so-called automated market makers (AMMs), smart contracts that pool liquidity and process trades as atomic swaps of tokens. how it works. In the real world, everything is priced based on the law of supply and demand. As a result, market makers act as buyers and sellers of last resort. 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. A CFMM is described by a continuous trading function (also known as the invariant, AMM invariant, or CFMM invariant). When traders make trades, they The job of the pool is to give Order book-based exchanges have a path-dependent price discovery process where the price of an asset depends on the behavioral responses of participants. 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Book exchanges which assets to be traded, AMMs function by using self-executing computer,! Financial markets buyers and sellers of last resort on different invariance properties under scaling traded on a decentralized (! Function looks like a zoomed-in hyperbola alleviate this problem of limited liquidity by liquidity... Sellers are also willing to sell at the top of the page from.