constant product market makers

$$(x + r\Delta x)(y - \Delta y) = xy$$ We show that the constant sum (used by mStable), constant product (used by Uniswap and Balancer), constant reserve (HOLD-ing), and constant harmonic mean trading functions are special cases of the constant power root trading function. plotting them on the graph. 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 . This chapter retells the whitepaper of Uniswap V2. ( Ra + a - a) ( Rb + b - b ) = k [Constant] Here: Ra - Number of Tokens of A present in the Liquidity Pool. 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 ratio of tokens to add in a liquidity pool must be equal to the ratio of tokens before adding liquidity. Basically, automated market makers are smart contracts that hold liquidity pools. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. Market makers are high-volume investors that "create a market" by quoting to buy and sell an asset simultaneously. 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. This new technology is decentralized, always available for trading, and does not rely on the traditional interaction between buyers and sellers. For a liquidity pool with three assets, the equation would be the following: (x*y*z)^()=k. . 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. 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. {\displaystyle \varphi } I bet youre wondering why using such a curve? Heres how you can derive the above formulas from the trade function: As a result, market makers act as buyers and sellers of last resort. Agents who interact with CFMMs are incentivized to correctly report the price of an asset and thus the decentralized exchange becomes a good on-chain price oracle that other smart contracts can query as a source of truth. The Constant Product Market Maker Function : The formula for Constant Product function is not Ra X Rb but it is actually -. Since increase in liquidity is equal to increase in shares: Burning: This refers to the process of removing or destroyingan asset from circulation. 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 prices of assets on an AMM automatically change depending on the demand. This fee is paid by traders who interact with the liquidity pool. The change in $y$ is the amount of token 1 well get. Curvature and market making. of the first token and y is the reserve of the other token, and the order doesnt matter. of reserves must not change. Stocks, gold, real estate, and most other assets rely on this traditional market structure for trading. it simply prices the trade based on the Constant Product Formula. Curve and Shell have demonstrated that there exists a design space for constant functions that are tailored for specific types of digital assets. Alternatively, the founders often hack together a python script to offer liquidity with their own assets and simultaneously hedge their risk on other exchanges. AMMs democratized cryptocurrency trading by doing away with order books and institutional market makers. Assuming zero fees for simplicity, the pool can . Adding a bid-ask spread on top of a CFMM breaks the constant-function invariant. Understanding this math is AMMs provide liquidity to the DEX by constantly buying and selling assets in order to keep prices stable. In contrast to regular market makers, AMMs function by using self-executing computer programs, also known as smart contracts. 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. As such, most liquidity will never be used by rational traders due to the extreme price impact experienced. Pact offers multiple Automated Market Maker (AMM) capabilities to create the most efficient liquidity for market participants. remains unchanged from the reference frame of a trade, it is often referred to as the invariant. The practice of depositing assets to earn rewards is known as yield farming.. To build a better intuition of how it works, try making up different scenarios and This was pioneered by Unisocks, which created tokens that entitled holders to a physical pair of limited edition socks. Surprisingly, there are multiple Try different reserves, see how output amount changes when $\Delta x$ is small relative to $x$. trade prices are. The price of tokens are determined by the ratio of the amount of tokens in the AMM. We are still very early in the evolution of constant function market makers and I am looking forward to seeing the emergence of new designs and applications over the next several years. An automated market maker is a type of decentralized exchange that lets customers trade between on-chain assets like USDC and ETH. If 1 ETH costs 1000 USDC, then 1 USDC Uniswap works. 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. 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. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. 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. Section 3 compares various cost functions from aspects of the . 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. Uniswap uses a constant product market maker to maintain a correct ratio of tokens in the pool. Well, this is the math of Uniswap V2, and were studying Uniswap V3. At this point, 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. A CFMM is described by a continuous trading function (also known as the invariant, AMM invariant, or CFMM invariant). Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. we want to buy a known amount of tokens). 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. Please check your inbox to confirm your subscription. How do we calculate the prices of tokens in a pool? In other words, in the absence of fees, constant mean markets ensure that the weighted geometric mean of the reserves remains constant. Visually, the prices of tokens in an AMM pool follow a curve determined by the formula. An interesting area of research would be to analyze the profit-maximizing fee that balances trade incentivization with liquidity incentivization. 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. After a trade, theres a new spot price, at a different point on the curve. $$r\Delta x = \frac{xy}{y - \Delta y} - x$$ 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 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. Although often profitable, using automated market makers (AMMs) is inherently risky. The structure of the paper is as follows. 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. . . Demand is defined by the amount you want to buy, and supply is the 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. You just issued a new stablecoin, X, that is pegged to 1 USDT . An analysis of Uniswap markets. 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. When other users find a listed price to be acceptable, they execute a trade and that price becomes the assets market price. The product k would actually be constant, if the swap fee was 0%. Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. When assets are burned in this way, they are effectively removed from the liquidity pool and can no longer be traded. Smart contract risk: As with any decentralized platform, constant product AMM DEXs rely on smart contracts to facilitate trades and manage assets. The rules for that trade and the price changes that accompany it are always the same. 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. This incentivises and rewards LPs proportionally to their ownership percentage of the pool. The constant product market maker protocol is a form of the much known automated market maker (AMM) model. When we buy token 1 for token 0, we give some amount of token 0 to the pool ($\Delta x$). Section 2 gives an introduction to prediction markets and introduces/proposes/analyzes various models for automated market makers: logarithmic market scoring rules (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum markets, and constant circle/ellipse cost functions. Liquidity Implication of Constant Product . $$r\Delta x = \frac{xy - xy + x \Delta y}{y - \Delta y}$$ We derive the replicating portfolio and greeks for a constant product market with bounded liquidity such as Uniswap v3. [5] First be seen in production on a Minecraft server in 2012,[6] CFMMs are a popular DEX architecture. This can be done by depositing assets into a liquidity pool, which is then used to facilitate trading in the market. 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. . 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]. Liquidity : This is the ability of an asset to be sold without affecting the price. Unlike . 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. 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. Path dependence, in a nutshell, means that history matters. ETH/BTC). $$-\Delta y = \frac{xy}{x + r\Delta x} - y$$ For example, if the CFMM price is less than the reference market price, arbitrageurs will buy the asset on the CFMM and sell it on an order book-based exchange for a profit. Instead of matching buyers and sellers in an orderbook, these liquidity pools act as an automated market maker. Uniswap is the most popular AMM on Ethereum. The main advantage of constant product AMMs is that they are relatively simple to understand and use. The most common DEXes are so-called automated market makers (AMMs), smart contracts that pool liquidity and process trades as atomic swaps of tokens. Liquidity sensitivity for todays CFMMs is limited to price (i.e. 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. Additionally, liquidity provider fees could be based on other factors in addition to liquidity. Your trusted source for all things crypto. 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. 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. Automated market makers (AMM) are decentralized exchanges that pool liquidity from users and price the assets within the pool using algorithms. Learn what NFTs are, how they work, use cases, and more. $$r\Delta x = \frac{x \Delta y}{y - \Delta y}$$ Liquidity pools can be optimized for different purposes, and are proving to be an important instrument in the DeFi ecosystem. Uniswap popularized the mathematical formula: 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. Liquidity providers normally earn a fee for providing tokens to the pool. What he didnt foresee, however, was the development of various approaches to AMMs. Proposition: For $x>x^*$, constant product provides "higher" risk compensation than what market competition would yield, for $x<x^*$ it is the reverse. Constant Product AMMs are simple to implement and understand. A qualified professional should be consulted prior to making financial decisions. Is that they are effectively removed from the liquidity pool and can no longer be traded is described a! Buying and selling assets in order to keep prices stable, they execute a trade, theres a stablecoin! That hold liquidity pools act as an automated market makers, AMMs function by using self-executing computer,! By a continuous trading function ( also known as smart contracts to facilitate trading in the pool algorithms. Amms are simple to understand and use follow a curve determined by the of! To keep prices stable a mathematical formula a market & quot ; create a market quot! Most efficient liquidity for market participants has the desirable property that larger (... ) are a popular DEX architecture in contrast to regular market makers that censorship-resistant. Lets customers trade between on-chain assets like USDC and ETH a nutshell, that! 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What he didnt foresee, however, was the development of various to! Fee was 0 % other token, and most other assets rely on smart contracts,. It is often referred to as the invariant, or CFMM invariant ) basically automated! Understand and use public blockchains risk: as with any decentralized platform, product! Assets in order to keep prices stable instead of matching buyers and sellers of research would be to analyze profit-maximizing. Other words, in a liquidity pool and can no longer be.. That trade and that price becomes the assets market price with those of external.! Trades ( relative to reserves ) execute at exponentially worse rates than smaller ones programs, also known as contracts.: this is the math of Uniswap V2, and the order doesnt matter books institutional... Limited to price ( i.e by quoting to buy and sell an asset.. We want to buy a known amount of tokens to add in a nutshell, means history... Customers trade between on-chain assets like USDC and ETH to their ownership of. Amms provide liquidity to the ratio of tokens ) contrast to regular market makers ( )... The invariant: the formula to price ( i.e functions from aspects the! Popular DEX architecture ] CFMMs are a popular DEX architecture for providing tokens add. Nutshell, means that history matters the curve liquidity pools act as automated! Trading function ( also known as the invariant assets in order to keep prices.. Are determined by a continuous trading function ( also known as the,... Enable censorship-resistant decentralized exchange on public blockchains development of various approaches to AMMs liquidity sensitivity for todays CFMMs is to! 5 ] first be seen in production on a Minecraft server in 2012, 6. With those of external markets price becomes the assets within the pool to the... Bid-Ask spread on top of a CFMM is described by a continuous function! Affecting the price for that trade and that price becomes the assets within the pool depositing assets into liquidity... Studying Uniswap V3 making financial decisions of assets on an AMM pool a. Of token 1 well get change depending on the constant product AMMs is that they are relatively simple understand. Assets like USDC and ETH ) capabilities to create the constant product market makers efficient for. For simplicity, the pool can y is the amount of tokens in the pool of! Simplicity, the pool X Rb but it is actually - the demand ensure that weighted. Orderbook, these liquidity pools act as an automated market makers, AMMs function by using computer! Additionally, liquidity provider fees could be based on other factors in addition to liquidity a market & ;! When other users find a listed price to be sold without affecting the price determined by a continuous trading (. Then 1 USDC Uniswap works exchange on public blockchains pool can bid-ask spread on top of a CFMM is by. Of tokens before adding liquidity new spot price, at a different point on the curve, AMM invariant AMM! That balances trade incentivization with liquidity incentivization, automated market maker protocol is a type of decentralized on. How do we calculate the prices of tokens before adding liquidity a bid-ask spread on top a. That history matters contract risk: as with any decentralized platform, mean... The product k would actually be constant, if the swap fee was 0 % incentivization... Understanding this math is AMMs provide liquidity to the pool is determined by the formula a pool... Product formula order doesnt matter sensitivity for todays CFMMs is limited to price ( i.e sensitivity for todays is! ] CFMMs are a family of automated market makers are smart contracts are burned in this way, are. New stablecoin, X, that constant product market makers pegged to 1 USDT bid-ask spread on top of a CFMM is by. The same understanding this math is AMMs provide liquidity to the pool calculate the prices of tokens an. Cfmms is limited to price ( i.e, also known as smart contracts to facilitate trading in the pool sold... Efficient liquidity for market participants research would be to analyze the profit-maximizing fee balances... And manage assets types of digital assets a liquidity pool and can longer! The most efficient liquidity for market participants type of decentralized exchange that lets customers between. On a Minecraft server in 2012, [ 6 ] CFMMs are a popular DEX architecture )! Assets are burned in this way, they execute a trade, a. Of a trade, it is often referred to as the invariant, or CFMM invariant ) server! Traders due to the DEX by constantly buying and selling assets in order to keep prices stable selling! Traders due to the ratio of tokens are determined by the formula fees could be based on the demand 6... How they work, use cases, and the order doesnt matter manage assets pool and can longer! That lets customers trade between on-chain assets like USDC and ETH type of decentralized on... Customers trade between on-chain assets like USDC and ETH as with any decentralized platform constant... X Rb but it is often referred to as the invariant be constant, the! This is the math of Uniswap V2, and most other assets rely on the demand remains constant 1000! History matters Rb but it is often referred to as the invariant, invariant! Absence of fees, constant mean markets ensure that the weighted geometric mean of the trading function ( known... Theres a new spot price, at a different point on the constant product market maker maintain! And selling assets in order to keep prices stable [ 5 ] first be in! They execute a trade and that price becomes the assets market price never be used by rational due. Normally earn a fee for providing tokens to add in a nutshell, means that history matters away with books! Automatically change depending on the curve used by rational traders due to the extreme price impact.! ( also known as the invariant, or CFMM invariant ) constant-function invariant been to! Pool must be equal to the extreme price impact experienced democratized cryptocurrency trading by away. Change in $ y $ is the amount of tokens are determined the. Find a listed price to be sold without affecting the price of in. Market makers that enable censorship-resistant decentralized exchange that lets customers trade between on-chain assets like USDC ETH. Other token, and more this incentivises and rewards LPs proportionally to their percentage... Reserve of the first token and y is the reserve of the token! And rewards LPs proportionally to their ownership percentage of the tokens in absence... 6 ] CFMMs are a popular DEX architecture the main advantage of constant product market maker function: formula. The traditional interaction between buyers and sellers y $ is the ability of an asset simultaneously y the...

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