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. rst proved that constant mean market makers could replicate a large set of portfolio value functions. This is how markets work. In this model, the weighted geometric mean of each reserve remains constant. Minting: Minting refers to the process of creating a new asset or increasing the supply of an existing asset. Basically, automated market makers are smart contracts that hold liquidity pools. Please check your inbox to confirm your subscription. 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. 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. This helps ensure that users can always buy or sell an asset on the DEX, even if there aren't any other buyers or sellers at the moment. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have certain advantages over widely deployed constant product cost functions. However, the CFMM + spread will never underperform the CFMM without a spread (the latter of which will never compensate for opportunity cost). In this article I explain what Automated Market Makers are, and dive deep into Constant Product Market Makers. Liquidity implications of constant product market makers. The exact mechanics vary from exchange to exchange, but generally, AMMs offer deep liquidity, low transaction fees, and 100% uptime for as many users as possible. In fact, these formulas free us from calculating prices! Concluding from the law of supply and demand, high demand increases the priceand this is a property we need to have I bet youre wondering why using such a curve? $21. CFMMs are largely path-independent (assuming minimal fees), which means that the price of any two quantities depends only on those quantities and not on the path between them. 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. To build a better intuition of how it works, try making up different scenarios and An automated market maker facilitates trades and allows digital assets to be traded on a decentralized exchange (DEX). While it is true that Uniswap is an AMM, we could refer to it with more specificity. This leads to very high capital efficiency, but with the trade-off of requiring active participation and oversight of liquidity provisioning. 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. In non-custodial AMMs, user deposits for trading pairs are pooled within a smart contract that any trader can use for token swap liquidity. The above calculations might seem too abstract and dry. trade prices are. A trader could then swap 500k dollars worth of their own USDC for ETH, which would raise the price of ETH on the AMM. 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. What Are Automated Market Makers (AMMs)? 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. The practice of depositing assets to earn rewards is known as yield farming.. AMMs fix this problem of limited liquidity by creating liquidity pools and offering. pool reserves. $$r\Delta x = \frac{xy}{y - \Delta y} - x$$ 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]. {\displaystyle \varphi } The first AMM were developed by Shearson Lehman Brothers and ATD. AMMs are a financial tool unique to Ethereum and decentralized finance (DeFi). The Constant Product Market Maker Function : The formula for Constant Product function is not Ra X Rb but it is actually -. 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. This loss occurs when the market-wide price of tokens inside an AMM diverges in any direction. This design ensures that the pool remains balanced according to its pre-set weights for each asset. The converse result was later proven, providing a mechanism for constructing a . Your trusted source for all things crypto. Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. Automated Market Making: Theory and Practice, Improved Price Oracles: Constant Function Market Makers, Research Partner @ 1kx // Alum Blockchain@Berkeley, Berkeley-Haas, studied extensively in academic literature, Explain the difference between automated market makers and constant function market makers, Explore the pros & cons of constant function market makers and discuss future directions of CFMM designs and use-cases, It provides a minimum representation of state: we only need to know the. The opposite happens to the price of BTC in an ETH-BTC pool. Not only do AMMs powered by Chainlink help create price action in previously illiquid markets, but they do so in a highly secure, globally accessible, and non-custodial manner. Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Jun Aoyagi and Yuki Ito. This type of AMM will adjust its exchange rates automatically based on demand and supply to maintain that ratio. This example is from the Desmos chart made by Dan Robinson, 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. 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. Uniswap and Constant Product Market Makers (CPMM) There are two assets, X and Y. Denote by x the volume of X and by y the volume of Y in the reserves. The prices of assets on an AMM automatically change depending on the demand. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged: Uniswap, Curve, and Balancer. "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. Since the intrinsic value exceeds the fair value of an equivalent derivative contract with a positive tenor, the CFMM bears an opportunity cost which must be compensated by volume across the bid-ask spread. a - Number of Tokens of A the trader has . Under this option, liquidity providers need to supply each token in the pair with an equal or 50:50 value. In effect, the function looks like a zoomed-in hyperbola. The same is true for any other pool, whether its a stablecoin pair or not (e.g. Theres a pool with some amount of token 0 ($x$) and some amount of token 1 ($y$). Even though Uniswap doesnt calculate trade prices, we can still see them on the curve. we want to buy a known amount of tokens). of the first token and y is the reserve of the other token, and the order doesnt matter. 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. The secret ingredient of AMMs is a simple mathematical formula that can take many forms. These pools are funded by liquidity providers so that the traders can trade against these pools. 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. This is due to the fact that a substantial portion of AMM liquidity is available only when the pricing curve begins to turn exponential. During periods of low volatility, Sigmadex can concentrate liquidity near the market price and increase capital efficiency, and then expand it during periods of high volatility to help protect traders from impairment loss. 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 Yes, I agree to receive email communications from Chainlink. 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. Uniswap popularized the mathematical formula: This mechanism ensures that Pact prices always trend toward the market price. 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 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. For example, a liquidity pool could hold ten million dollars of ETH and ten million dollars of USDC. AMM systems allow users to burn assets by removing them from a liquidity pool. StableSwap is a type of AMM invented by Curve Finance. Product-market fit is a moving target. This is true, Curvature and market making. V It's the nature of any competitive industry and the only constant is Change. This can be helpful for traders who want to make informed decisions about which assets to buy or sell. On this Wikipedia the language links are at the top of the page across from the article title. Constant Mean Market Maker (CMMM): It ensures the average price of assets in a particular market remains constant over time. Since the technology is still pretty new, am looking forward to seeing advancement in the technology and in the entire DeFi ecosystem. real estate). Their trading activity creates liquidity, lowering the price impact of larger trades. By incorporating multiple dynamic variables into its algorithm, it can create a more robust market maker that adapts to changing market conditions. the larger the liquidity pool, the lower the price slippage) but there are additional dimensions that could be dynamic. And when demand is low, the price is also lower. Hybrid CFMMs enable extremely low price impact trades by using an exchange rate curve that is mostly linear and becomes parabolic only once the liquidity pool is pushed to its limits. demand: the more tokens you want to remove from a pool (relative to pools reserves), the higher the impact of demand is. Well, this is the math of Uniswap V2, and were studying Uniswap V3. $$(x + r\Delta x)(y - \Delta y) = xy$$ 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. Balancer stretches the limits of Uniswap by allowing users to create dynamic liquidity pools of up to eight different assets in any ratio, thus expanding AMMs flexibility. ; Tarun Chitra, Guillermo Angeris, Alex Evans, and Hsien-Tang Kao. Constant Sum Market Maker (CSMM): These market makers ensure the sum of the assets in a particular market is constant.This is achieved by adjusting the prices of assets in the market based on the supply and demand of those assets. If we increase liquidity by 5% the shares also increase by 5 %. What is an automated market maker? 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. 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. Conversely, the price of BTC goes down as there is more BTC in the pool. (DEX). And this is where we need to bring the demand part back. Constant Product Market Maker (CPMM) The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. How do we calculate the prices of tokens in a pool? A constant sum market maker is a relatively straightforward implementation of a constant function market maker, satisfying the equation: Where R_i are the reserves of each asset and k is a constant. Liquidity risk: As with any market, the prices of assets on a constant product AMM DEX are subject to supply and demand. Because of this matching process, there is the possibility that some orders may take a while to get filled, if ever. and states that trades must not change the product (. Constant Product Market Maker (CPMM) - Pact GitBook Constant Product Market Maker (CPMM) Pact offers a familiar Constant Product Market Maker (CPMM) capability. These CFMMs will have price functions that best reflect the characteristics of their respective assets, resulting in less slippage and more efficient exchange. We focus particularly on separability and on different invariance properties under scaling. Dont be scared by the long name! AMMs provide liquidity to the DEX by constantly buying and selling assets in order to keep prices stable. Various types of AMMs are examined, including: Constant Product Market Makers; Constant Mean Market Makers; Constant Sum Market Makers; Hybrid Function Market Makers; and, Dynamic Automated Market Makers. are the pricing functions that respect both supply and demand. Lets visualize the constant product function to better understand 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 first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. In this video, we explain how constant product automated market makers using a very simple story so you can. On a traditional exchange platform, buyers and sellers offer up different prices for an asset. it simply prices the trade based on the Constant Product Formula. For example, Bancor 3 has integrated Chainlink Automation to help support its auto-compounding feature. This allows for variable exposure to different assets in the pool and enables swaps between any of the pools assets. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. Thank you for signing up! 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 . Alternatively, the founders often hack together a python script to offer liquidity with their own assets and simultaneously hedge their risk on other exchanges. collateralized options) and security tokens (e.g. In Vitalik Buterins original post calling for automated or. $$-\Delta y = \frac{- y r \Delta x}{x + r\Delta x}$$ CFMMs provide the ability to measure the price of an asset without the use of a central third party, addressing a problem often known as the oracle problem. CPMMs are based on the function x*y=k, which establishes a range of prices for two tokens according to the available quantities (liquidity) of each token. These An early description of a CFMM was published by economist Robin Hanson in "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation" (2002). Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as . A liquidity pool is a smart contract that holds reserves of two or more tokens and allows anyone to deposit and withdraw funds from them, but only according to very specific rules. Curve (a.k.a. When expanded it provides a list of search options that will switch the search inputs to match the current selection. 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. 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. Still neglecting fees, let's imagine that after some trading, the price has changed; 1 ETH is now worth 120 DAI. 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. We derive the value function for liquidity providers . is a "consistent payoff function",[8] that is, a payoff function which is concave, nonnegative, nondecreasing, and 1-homogenous, it is possible to construct a trading function which achieves 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. In the real world, everything is priced based on the law of supply and demand. $$\Delta x = \frac{x \Delta y}{r(y - \Delta y)}$$. 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. Section 3 compares various cost functions from aspects of the . the incentive to supply these pools with assets. Constant product AMMs use a formula based on the "constant product" concept to set the prices of assets. It can be called a hybrid AMM since it uses elements from both the constant product and constant sum market makers. How does the Constant Product Market Maker (CPMM) work? 1.0.0. . Users trade against the smart contract (pooled assets) as opposed to directly with a counterparty as in order book exchanges. Uniswap V2 / constant-product AMM implemented in Solana's Anchor -- add and remove liquidity, swap tokens, earn fees! is calculated differently. As a result, market makers act as buyers and sellers of last resort. It is also common to hear the term bonding curve when talking about CFMMs but it is incorrect to do so. {\displaystyle \varphi } 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. The more assets in a pool and the more liquidity the pool has, the easier trading becomes on decentralized exchanges. Liquidity provider: is an entity that provides assets to the AMM in order to increase the liquidity of a particular market and earn a small fee. 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. In order to understand a constant product AMM, we first need to understand what is a market maker. (the token they want to buy). arxiv: 1911.03380 [q-fin.TR] Google Scholar; Jun Aoyagi and Yuki Ito. This risk can be especially pronounced in markets with low liquidity, or in times of market volatility. Many thanks to Tom Schmidt, Tarun Chitra, Guillermo Angeris, and Dan Robinson for their feedback on this piece. A constant product market maker, first implemented by Uniswap, satisfies the equation: Where R_ and R_ are reserves of each asset and is the transaction fee. 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. In 2020, the term yield farming did not exist. of Uniswap V3 is different. A qualified professional should be consulted prior to making financial decisions. This fee is paid by traders who interact with the liquidity pool. The Conceptual Flaws of Constant Product Automated Market Making Andreas Park June 8, 2021 Abstract Blockchain-based decentralized exchanges are a pre-requisite and the backbone of decentralized nance. 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. When plotted, the constant product function is a quadratic hyperbola: Where axes are the pool reserves. Assuming zero fees for simplicity, the pool can . However, the execution price is 0.666, so we get only 133.333 of token 1! We can always find the output amount using the $\Delta y$ formula A simple and secure platform to build your crypto portfolio. 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. This implies a price of 1 ETH = 100 DAI. simple mathematical formula: $x$ and $y$ are pool contract reservesthe amounts of tokens it currently holds. A constant-function market maker (CFMM) is a market maker with the property that 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. 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. ingly e ective market maker appears to be the constant product market maker used by Uniswap [7], likely the rst and possibly the most popular implementation. ( Ra + a - a) ( Rb + b - b ) = k [Constant] Here: Ra - Number of Tokens of A present in the Liquidity Pool. AMMs have become a primary way to trade assets in the DeFi ecosystem, and it all began with a blog post about on-chain market makers by Ethereum founder Vitalik Buterin. . This new technology is decentralized, always available for trading, and does not rely on the traditional interaction between buyers and sellers. [8] It has been noted that this includes the intrinsic value of any negative-gamma derivative contract. For example, one could adjust LP fees based on trailing volatility, resulting in a stochastic pricing mechanism and the added benefit of volatility sensitivity for CFMMs. For example, Synthetix was able to use Uniswap to bootstrap liquidity for its sETH liquidity pool, giving users an easier way to begin trading on the exchange. $$r\Delta x = \frac{xy - xy + x \Delta y}{y - \Delta y}$$ 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. When assets are burned in this way, they are effectively removed from the liquidity pool and can no longer be traded. 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. This button displays the currently selected search type. 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. is increasing. 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. CFMMs are often used for secondary market trading and tend to accurately reflect, as a result of arbitrage, the price of individual assets on reference markets. AMM systems allow users to mint new assets by providing liquidity to the AMM in the form of other assets. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. So in the next part, well see how the mathematics crucial to build a Uniswap-like DEX, but its totally fine if you dont understand everything at this stage. 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. 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. Every trade starts at the point on the curve that corresponds to the current ratio of Order book-based exchanges have a path-dependent price discovery process where the price of an asset depends on the behavioral responses of participants. $$r\Delta x = \frac{xy - x(y - \Delta y)}{y - \Delta y}$$ 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. 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. the price is also high. 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 . Smart contract developers even create front running bots just for this purpose.This can potentially distort the market and make it harder for the AMM to maintain the constant product. . You need to enable Javascript to view this site properly. When we buy token 1 for token 0, we give some amount of token 0 to the pool ($\Delta x$). The change in $y$ is the amount of token 1 well get. value doesnt matter. how it works. AMM users supply liquidity pools with crypto tokens, whose prices are determined by a constant mathematical formula. If an AMM doesnt have a sufficient liquidity pool, it can create a large price impact when traders buy and sell assets on the DeFi AMM, leading to capital inefficiency and impermanent loss. Liquidity sensitivity for todays CFMMs is limited to price (i.e. it doesnt matter which of them is 0 and which is 1. For example, the proposed market makers are more robust against slippage based front running attacks. Constant Product AMMs are simple to implement and understand. $$r\Delta x = \frac{x \Delta y}{y - \Delta y}$$ . This property implies that market makers should adjust the elasticity of their pricing response based on the volume of activity in the market. Curve offers low-price-impact swaps between tokens that have a relatively stable 1:1 exchange rate. The CPMM spreads liquidity out equally between all prices, automatically adjusting the price in the . One alternative approach could be to increase the LP fee at lower levels of liquidity to incentivize LPs to deposit their assets (e.g. . As the legend goes, Uniswap was invented in Desmos. {\displaystyle V} 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. 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. The law of supply and demand tells us that when demand is high (and supply is constant) 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. 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. We should focus on what works now and assume that it might not work in the future.
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