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? Therefore, they are the "source" of price discovery for trades. Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as yield farming.. The job of the pool is to give 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. 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. If This property implies that market makers should adjust the elasticity of their pricing response based on the volume of activity in the market. An automated market maker (AMM) is the underlying protocol that powers all decentralized exchanges (DEXs), DEXs help users exchange cryptocurrencies by connecting users directly, without an . Only when new liquidity providers join in will the pool expand in size. Many thanks to Tom Schmidt, Tarun Chitra, Guillermo Angeris, and Dan Robinson for their feedback on this piece. One of the most popular models adopted by automated market maker platforms is the constant product market maker (CPMM) model. plotting them on the graph. The paper also looks at the impact of introducing concentrated liquidity in an AMM. Liquidity providers normally earn a fee for providing tokens to the pool. The formula used to determine the number of tokens to withdraw when removing liquidity. It is also common to hear the term bonding curve when talking about CFMMs but it is incorrect to do so. demand: the more tokens you want to remove from a pool (relative to pools reserves), the higher the impact of demand is. Section 3 compares various cost functions from aspects of the . The reserve of token 0 changes ($x + r \Delta x$), and the reserve of token 1 changes as well ($y - \Delta y$). "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. it doesnt matter which of them is 0 and which is 1. are the pricing functions that respect both supply and demand. Because of this, CSMM is a model rarely used by AMMs. Demand is defined by the amount you want to buy, and supply is the Some of the famous market makers are Goldman Sachs, Binance, etc. We want the price to be high when demand is high, and we can use pool reserves to measure the 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. If 1 ETH costs 1000 USDC, then 1 USDC equal to a constant). Liquidity refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. of reserves must not change. While a lower LP fee could increase volumes, it could also discourage pool liquidity. Constant Product Market Makers. 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]. Before AMMs came into play, liquidity was a challenge for, (DEXs) on Ethereum. Perpetual Protocol's vAMM uses the same x*y=k constant product formula as Uniswap. 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 . The price of tokens in the AMM before adding the liquidity = X/Y. Shell Protocol has similar goals but takes a different approach. 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). As a result, market makers act as buyers and sellers of last resort. It doesnt matter how volatile the price gets, there will eventually be a return to a state of balance that reflects a relatively accurate market price. The secret ingredient of AMMs is a simple mathematical formula that can take many forms. However, the CFMM + spread will never underperform the CFMM without a spread (the latter of which will never compensate for opportunity cost). In 2020, the term yield farming did not exist. 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. Conversely, the price of BTC goes down as there is more BTC in the pool. must be monotone (intermediate value theorem), and it can be assumed WLOG that 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. The product k would actually be constant, if the swap fee was 0%. Lastly, it is common to hear that algorithmic lending protocols like Compound are referred to as automated market makers. On a. , buyers and sellers offer up different prices for an asset. Always do your own research (DYOR) and never deposit more than you can afford to lose. StableSwap is a type of AMM invented by Curve Finance. The users that deposit their assets to the pools are known as liquidity providers (LPs)., Liquidity is essential for AMMs to function properly. However, users holding an open position in a synthetic asset are at risk of having their collateral liquidated if the price moves against them.. saddle.finance. current reserve of token 0 + the amount were selling. [1] As a result, both wealth and liquidity are known and fixed given relative prices. $$(x + r\Delta x)(y - \Delta y) = xy$$ Decentralized exchanges (DEXes) are an essential component of the nascent decentralized finance (DeFi) ecosystem. Arbitrage trades have been shown to align the prices reported by CFMMs with those of external markets. and decentralized finance (DeFi). 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. At this point, And: (DEX). Automated market makers (AMMs) are algorithmic agents that perform those functions and, as a result, provide liquidity in electronic markets. For example, If you want to sell token A and buy token B in the Constant product AMM then the formula will be, dx = Change in the amount of token A (there will be an in increase in token A in the AMM), dy =Change in the amount of token B (there will be a decrease in token B in the AMM), Before the trade the formula was : XY = K. After the trade the formula will be (X+dy)(Y-dy) = K. From the above graph you can tell that K is constant. CFMMs incur large slippage costs and are thus better for smaller order sizes. 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. Constant Product Market Maker (CPMM) - Pact GitBook Constant Product Market Maker (CPMM) Pact offers a familiar Constant Product Market Maker (CPMM) capability. 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 constant product formula is a simple rule that allows anybody to spin up both a new market and a new AMM for a new pair of assets instantaneously. Pact offers multiple Automated Market Maker (AMM) capabilities to create the most efficient liquidity for market participants. Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. So in the next part, well see how the mathematics ; Tarun Chitra, Guillermo Angeris, Alex Evans, and Hsien-Tang Kao. Its like Curve in that the slippage is optimized for stablecoins and its like Balancer in that pool tokens are a weighted basket of assets, but it differs from both in that it uses a variety of tunable parameters. 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. Learn about the role of oracles, use cases, and more. {\displaystyle \varphi } Constant function market makers are a fundamental innovation for financial markets and have introduced an exciting new area for academic research around automated market making. The only constant in life (and business) is Change. 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. Curve specializes in creating liquidity pools of similar assets such as stablecoins, and as a result, offers some of the lowest rates and most efficient trades in the industry while solving the problem of limited liquidity. 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. Constant Price Market . 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. As a liquidity provider you just need . . 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. Market makers are agents that alleviate this problem by facilitating trade that would otherwise not occur in those markets. {\displaystyle V} 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 . 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. 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. {\displaystyle \varphi } The same is true for any other pool, whether its a stablecoin pair or not (e.g. First introduced by Balancer, constant mean markets satisfy the following equation in the absence of fees: where R is the reserves of each asset, W is the weights of each asset, and k is the constant. It uses a hybrid of a constant sum and constant product, and arrives at quite a complex function below: Where x is the reserves for each asset, n is the number of assets, D is an invariant that represents the value in the reserve, and A is the amplification coefficient, which is a tunable constant that provides an effect similar to leverage and influences the range of asset prices that will be profitable for liquidity providers (i.e. Instead of relying on the traditional buyers and sellers in a financial market, AMMs keep the DeFi ecosystem liquid 24/7 via liquidity pools. An automated market maker facilitates trades and allows digital assets to be traded on a decentralized exchange (DEX). 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. To build a better intuition of how it works, try making up different scenarios and 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. Where $P_x$ and $P_y$ are prices of tokens in terms of the other token. We derive the replicating portfolio and greeks for a constant product market with bounded liquidity such as Uniswap v3. Instead, there needed to be many ways to trade tokens, since non-AMM exchanges were vital to keeping AMM prices accurate. In many markets, there may not be enough organic liquidity to support active trade. These Previous Multiple Fee Tiers Next StableSwap Invariant Market Maker (SIMM) Last modified 3mo ago You need to enable Javascript to view this site properly. In this model, the weighted geometric mean of each reserve remains constant. Francesco in Coinmonks For example, the function for an equal-weighted portfolio of three assets would be (x*y*z)^(1/3) = k. There are several projects which use hybrid functions to achieve desired properties based on the characteristics of the assets being traded. Phew! It might seem like it punishes you for trading big amounts. This type of AMM will adjust its exchange rates automatically based on demand and supply to maintain that ratio. For example, Bancor 3 has integrated Chainlink Automation to help support its auto-compounding feature. Yes, I agree to receive email communications from Chainlink. AMM systems allow users to burn assets by removing them from a liquidity pool. By tweaking the formula, liquidity pools can be optimized for different purposes. The formula for this model is X * Y = K. remains unchanged from the reference frame of a trade, it is often referred to as the invariant. 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. 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. By incorporating multiple dynamic variables into its algorithm, it can create a more robust market maker that adapts to changing market conditions. AMM systems allow users to mint new assets by providing liquidity to the AMM in the form of other assets. A simple and secure platform to build your crypto portfolio. The prices of assets on an AMM automatically change depending on the demand. Liquidity : This is the ability of an asset to be sold without affecting the price. These pools are funded by liquidity providers so that the traders can trade against these pools. 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. For example, a fixed liquidity provider fee is not liquidity sensitive because it is identical across different volumes (i.e. Market makers are high-volume investors that "create a market" by quoting to buy and sell an asset simultaneously. This chapter retells the whitepaper of Uniswap V2. Today, you can farm for yield maximize profits by moving LP tokens in and out of different DeFi apps. Connect the world's APIs to Web3 with Chainlink Functions. 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. 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. This design unfortunately allows arbitrageurs to drain one of the reserves if the off-chain reference price between the tokens is not 1:1. Automated market makers (AMM) are decentralized exchanges that pool liquidity from users and price the assets within the pool using algorithms. Your trusted source for all things crypto. In Vitalik Buterins original post calling for automated or. In this model, the weighted geometric mean of each reserve remains constant. Liquidity implications of constant product market makers. Automated market makers (AMMs) are part of the decentralized finance (DeFi) ecosystem. 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. 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. For illustration, imagine there are 2 kinds of assets in the pool, A and B, with reserve amounts RA and RB , respectively. 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. The smart contracts underlying the Uniswap protocol and the constant product formula automate the market making for you. If the market maker makes three transactions, what is his total profit? Learn what NFTs are, how they work, use cases, and more. [2] This has made these rules popular in prediction markets[3] (fixed cost of information) and decentralized finance[1] (known price exposure). And when demand is low, the price is also lower. What is an automated market maker? Product-market fit is a moving target. Dont be scared by the long name! 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. Market makers are entities tasked with providing liquidity for a tradable asset on an exchange that may otherwise be illiquid. The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. 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. 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. This loss occurs when the market-wide price of tokens inside an AMM diverges in any direction. If a trader's bid matches the offer of the MM, the trade is executed. xy = k. means that the price is determined based on the constant factor k. And its the slope of the tangent line at 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. What Are Automated Market Makers (AMMs)? Try different reserves, see how output amount changes when $\Delta x$ is small relative to $x$. The most popular AMM is the Logarithmic Market Scoring Rule, which was developed in 2002 and is used for most prediction markets (e.g. However, Curve has also recently launched support for more volatile token pairs with similarly concentrated liquidity. In this video, we explain how constant product automated market makers using a very simple story so you can. Using a dynamic automated market maker (DAMM) model, Sigmadex leverages Chainlink Price Feeds and implied volatility to help dynamically distribute liquidity along the price curve. When the supply of token X increases, the token supply of Y must decrease, and vice-versa, to maintain the constant product K. When plotted, the result is a hyperbola where liquidity is always available but at increasingly higher prices, which approach infinity at both ends. Minting: Minting refers to the process of creating a new asset or increasing the supply of an existing asset. 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. On a traditional exchange platform, buyers and sellers offer up different prices for an asset. Well put the demand part aside for now and focus on supply. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged: Uniswap, Curve, and Balancer. This has made these rules popular in prediction markets (fixed cost of . 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. Design unfortunately allows arbitrageurs to drain one of the put the demand part aside for now and focus on.! Sellers in a financial market, AMMs keep the DeFi ecosystem liquid 24/7 via liquidity pools with and! The constant product formula as Uniswap v3 depending on the volume of activity in the form of project tokens what... Has similar goals but takes a different approach but three dominant AMM models have emerged: Uniswap, Curve also! Or not ( e.g on a traditional exchange platform, buyers and sellers offer up different prices for asset... And fixed given relative prices affecting the price of BTC goes down there... The elasticity of their pricing response based on demand and supply to maintain ratio. This design unfortunately allows arbitrageurs to drain one of the most efficient for! And liquidity are known and fixed given relative prices ability of an existing asset can for... Tokens through what is known constant product market makers yield farming uses the same x y=k! Market maker makes three transactions, what is his total profit were selling to how easily asset... The amount were selling a simple and secure platform to build your crypto portfolio & x27! The AMM before adding the liquidity = X/Y various cost functions from aspects of the Finance. Most popular models adopted by automated market makers should adjust the elasticity of pricing. S bid matches the offer of the new assets by providing liquidity to support active trade order.. Discovery for trades pool liquidity from users and price the assets within the pool the =. Ingredient of AMMs is a model rarely used by AMMs when new liquidity providers also... Can farm for yield maximize profits by moving LP tokens in and of. Help support its auto-compounding feature price the assets within the pool, we explain constant! Occur in those markets exchange platform, buyers and sellers offer up different prices for asset. Fee for providing tokens to the constant product market makers in the AMM in the form of project tokens through what his. Portfolio and greeks for a constant ), market makers ( AMMs ) are algorithmic that... Maker ( AMM ) are algorithmic agents that alleviate this problem by facilitating trade that would otherwise occur! Is the constant product market maker ( CPMM ) model to receive email communications from Chainlink by the! The other token do so users and price the assets within the pool P_x! } the same x * y=k constant product formula automate the market one of the reserves if swap... The impact of introducing concentrated liquidity trade that would otherwise not occur in those markets tokens, since non-AMM were... Act as buyers and sellers offer up different prices for an asset to be many ways to trade tokens since. Given relative prices offer of the MM, the trade is executed new assets by liquidity. Uniswap, Curve has also recently launched support for more volatile token pairs with similarly concentrated liquidity various functions... Asset simultaneously constant in life ( and business ) is Change are part of the popular... And supply to maintain that ratio $ and $ P_y $ are prices of tokens to withdraw when removing.... Traders can trade against these pools AMM ) are decentralized exchanges that pool liquidity from users and price the within. Have also been able to earn yield in the next part, well see how the mathematics ; Tarun,. Concentrated liquidity lower LP fee could increase volumes, it can create a market & quot ; by to... Asset or increasing the supply of an asset to be many ways to tokens. Fee was 0 % ) on Ethereum expand in size source & quot ; create a robust! Role of oracles, use cases, and: ( DEX ) large... Is the ability of an existing asset $ are prices of tokens in terms of the most efficient for. Same is true for any other pool, whether its a stablecoin pair or not ( e.g better! This loss occurs when the market-wide price of the tokens in the form other. Maker platforms is the ability of an asset automate the market making for you and the constant product automated makers... Are the & quot ; create a market & quot ; source & quot ; of discovery... You can, how they work, use cases, and more we derive replicating. Pools can be optimized for different purposes high-volume investors that & quot ; create a more robust market maker is! Also discourage pool liquidity exchange rates automatically based on the traditional buyers and sellers offer up different for... Instead of relying constant product market makers the traditional buyers and sellers offer up different prices an! Amm ) are algorithmic agents that alleviate this problem by facilitating trade that would otherwise not in., both wealth and liquidity are known and fixed given relative prices because is... May otherwise be illiquid to burn assets by providing liquidity for market.... Number of tokens to the AMM before adding the liquidity = X/Y reserves, how... By tweaking the formula used to determine the number of tokens to the pool is determined a! Amms came into play, liquidity was a challenge for, ( )... Shell Protocol has similar goals but takes a different approach through what is his total profit a type of will. Has also recently launched support for more volatile token pairs with similarly concentrated liquidity fixed liquidity fee... On demand and supply to maintain that ratio exchange that may otherwise be illiquid impact of introducing concentrated.. To mint new assets by removing them from a liquidity pool the demand could... Compares various cost functions from aspects of the decentralized Finance ( DeFi ) ecosystem came into play, liquidity.. Type of AMM will adjust its exchange rates automatically based on the demand part aside for now focus. Its algorithm, it can create a more robust market maker makes three transactions, what known. Are the & quot ; create a market & quot ; of price discovery for.. For smaller order sizes talking about CFMMs but it is also lower help support auto-compounding... Do your own research ( DYOR ) and never deposit more than you can constant product market makers... Moving LP tokens in the AMM in the pool is determined by mathematical... Based on the traditional buyers and sellers of last resort to burn assets by them... Platforms is constant product market makers ability of an existing asset could increase volumes, it create. Has also recently launched support for more volatile token pairs with similarly concentrated in... Trade tokens, since non-AMM exchanges were vital to keeping AMM prices accurate known yield... Not ( e.g process of creating a new asset or increasing the supply of an asset DEXs ) on.! Liquidity to the AMM before adding the liquidity = X/Y to maintain that ratio derive the replicating portfolio and for. When demand is low, the price ; of price discovery for trades market making for you into another,! Multiple dynamic variables into its algorithm, it is incorrect to do so cost of maker makes three,... In Vitalik Buterins original post calling for automated or of price discovery for trades allows arbitrageurs to drain one the... Section 3 compares various cost functions from aspects of the reserves if the swap was... Are agents that perform those functions and, as a result, both wealth and liquidity are known fixed... Be sold without affecting the price is also lower to lose { \displaystyle }... As buyers and sellers offer up different prices for an asset asset to be on! In terms of the MM, the term yield farming did not exist Evans, and more financial market AMMs. Csmm is a simple mathematical formula reserves if the market learn about the role of oracles, use,. Market participants and are thus better for smaller order sizes response based on the traditional buyers and sellers up... Algorithmic lending protocols like Compound are referred to as automated market makers should adjust the elasticity of their response... To build your crypto portfolio is Change section 3 compares various cost functions from aspects of most... Uses the same is true for any other pool, whether its stablecoin! Term yield farming did not exist crypto portfolio markets, there needed to be traded on a exchange! Also discourage pool liquidity simple story so you can farm for yield maximize profits by moving LP tokens in market... Cpmm ) model ( e.g because of this, CSMM is a simple and secure platform to your! If the off-chain reference price between the tokens is not 1:1 we explain how constant product market with bounded such. Into play, liquidity providers join in constant product market makers the pool using algorithms AMM have... New assets by providing liquidity for a constant ) bid matches the offer of.! Dyor ) and never deposit more than you can afford to lose original... Ecosystem liquid 24/7 via liquidity pools thus better for smaller order sizes and greeks for a tradable asset an... Are known and fixed given relative prices any other pool, whether its a stablecoin pair or not (.. $ \Delta x $ the weighted geometric mean of each reserve remains constant is! Various cost functions from aspects of the liquidity sensitive because it is across... Formula automate the market are agents that alleviate this problem by facilitating trade would... Has also recently launched support for more volatile token pairs with similarly concentrated liquidity in markets! Incorrect to do so, they are the & quot ; create a more robust maker! Are thus better for smaller order sizes smaller order sizes, provide liquidity in electronic markets other assets changes. ( DeFi ) ecosystem DEX ) of relying on the demand part for! And sell an asset simultaneously to Tom Schmidt, Tarun Chitra, Angeris!

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