If 1 ETH costs 1000 USDC, then 1 USDC 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. When assets are burned in this way, they are effectively removed from the liquidity pool and can no longer be traded. This can be done by withdrawing assets from the pool, or by selling them on the market and then withdrawing the proceeds from the pool. (the token they want to buy). 2019. This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. Oops! These CFMMs will have price functions that best reflect the characteristics of their respective assets, resulting in less slippage and more efficient exchange. 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. An automated market maker (AMM) is a system that automatically facilitates buy and sell orders on a decentralized exchange. means there is a constant balance of assets that determines the price of tokens in a liquidity pool. The product k would actually be constant, if the swap fee was 0%. {\displaystyle \varphi } The smart contracts underlying the Uniswap protocol and the constant product formula automate the market making for you. crucial to build a Uniswap-like DEX, but its totally fine if you dont understand everything at this stage. After a trade, theres a new spot price, at a different point on the curve. the price is also high. AMMs provide liquidity to the DEX by constantly buying and selling assets in order to keep prices stable. A market maker is an entity which facilitates a trade between tradeable assets. When does the tail wag the dog? Synthetix is a protocol for the issuance of synthetic assets that tracks and provides returns for another asset without requiring you to hold that asset. Constant product automated market makers (CPMM): These market makers use a fixed product formula to ensure that the value of a particular market remains constant. For example: in As such, most liquidity will never be used by rational traders due to the extreme price impact experienced. 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. Uniswap is the most popular AMM on Ethereum. 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. a - Number of Tokens of A the trader has . The reserve of token 0 changes ($x + r \Delta x$), and the reserve of token 1 changes as well ($y - \Delta y$). XY=K.The best example of a DEX that uses this is Uniswap and Bancor. Excessive Trading? The prices of tokens in a pool are determined by the supply of the tokens, that is by the amounts of reserves of the The prices of assets on an AMM automatically change depending on the demand. Proposition: For \(x>x^*\), constant product provides "higher" risk compensation than what market competition would yield, for \(x<x^*\) it is the reverse. Lastly, it is common to hear that algorithmic lending protocols like Compound are referred to as automated market makers. Concluding from the law of supply and demand, high demand increases the priceand this is a property we need to have . building one specific type of AMMConstant Function Market Maker. AMMs fix this problem of limited liquidity by creating liquidity pools and offering liquidity providers the incentive to supply these pools with assets. 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]. Path dependence, in a nutshell, means that history matters. 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. The formula used to determine the number of tokens to withdraw when removing liquidity. 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! 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. Liquidity refers to how easily one asset can be converted into another asset, often a fiat currency, without affecting its market price. Ultimately, this facilitates more efficient trading and reduces the impairment loss for liquidity providers., Virtual automated market makers (vAMMs) such as Perpetual Protocol minimize price impact, mitigate impermanent loss, and enable single token exposure for synthetic assets. We want the price to be high when demand is high, and we can use pool reserves to measure the If When they have a larger variation of the two assets they are more likely to experience that impermanent loss. Previous Multiple Fee Tiers Next StableSwap Invariant Market Maker (SIMM) Last modified 3mo ago 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. Market makers are agents that alleviate this problem by facilitating trade that would otherwise not occur in those markets. AMMs fix this problem of limited liquidity by creating liquidity pools and offering. With the Constant Product Market Maker (CPMM) capability, pairs act as automated market makers, ready to accept one token for the other as long as the constant product formula is preserved. Rb - Number of Tokens of B present in the Liquidity Pool. Most AMMs use a constant product market maker model. This means its solution is predominantly designed for stablecoins. Token prices are simply relations of reserves: $$P_x = \frac{y}{x}, \quad P_y=\frac{x}{y}$$. In effect, the function looks like a zoomed-in hyperbola. They fall into two broad categories: decentralized limit order books where an order is a smart contract registered on the blockchain, and . Well, this is the math of Uniswap V2, and were studying Uniswap V3. 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. Such prices are called spot prices and they only reflect current market prices. The first AMM were developed by Shearson Lehman Brothers and ATD. . Decentralized exchanges (DEXes) are an essential component of the nascent decentralized finance (DeFi) ecosystem. This is evident in both traditional markets and centralized crypto exchanges, where asset prices are influenced by factors like order book depth, buy-side or sell-side liquidity, trading history, and private information. This changes the reserves of the pool, and the constant function formula says that the product 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. Where $P_x$ and $P_y$ are prices of tokens in terms of the other token. $$\Delta x = \frac{x \Delta y}{r(y - \Delta y)}$$. Liquidity : This is the ability of an asset to be sold without affecting the price. The price of tokens in the AMM before adding the liquidity = X/Y. A simple and secure platform to build your crypto portfolio. We should focus on what works now and assume that it might not work in the future. You need to enable Javascript to view this site properly. 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. In other words, in the absence of fees, constant mean markets ensure that the weighted geometric mean of the reserves remains constant. Stocks, gold, real estate, and most other assets rely on this traditional market structure for trading. Eleven sellers are also willing to sell at the same prices. CSMMs follow the formula x+y=k, which creates a straight line when plotted. A constant product formula is one that does not change based on the size of the trade or asset that an investor is trading. Try different reserves, see how output amount changes when $\Delta x$ is small relative to $x$. Section 3 compares various cost functions from aspects of the . Constant Product Market Makers. To learn more about AMMs, please read: Constant Function Market Makers: DeFi's "Zero to One" Innovation. arxiv: 2012.08040 [q-fin.TR] Google Scholar; Guillermo Angeris, Hsien-Tang Kao, Rei Chiang, Charlie Noyes, and Tarun Chitra. value doesnt matter. The most common DEXes are so-called automated market makers (AMMs), smart contracts that pool liquidity and process trades as atomic swaps of tokens. Understanding this math is If there is not enough liquidity (i.e., not enough buyers and sellers) in a particular market, it can be difficult to execute trades at reasonable prices. over the inventory amounts (commonly referred to as reserves),[7] such that the market maker only accepts trades which leave The job of the pool is to give 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. Additionally, liquidity provider fees could be based on other factors in addition to liquidity. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged: Uniswap, Curve, and Balancer. As a result, both wealth and liquidity are known and fixed given relative prices. As a result, each trade also increases. And, magically, AMM users supply liquidity pools with crypto tokens, whose prices are determined by a constant mathematical formula. 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 If the AMM price ventures too far from market prices on other exchanges, the model incentivizes traders to take advantage of the price differences between the AMM and outside crypto exchanges until it is balanced once again. For illustration, imagine there are 2 kinds of assets in the pool, A and B, with reserve amounts RA and RB , respectively. 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. This chapter retells the whitepaper of Uniswap V2. how it works. 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. vAMMs use the same x*y=k constant product formula as CPMMs, but instead of relying on a liquidity pool, traders deposit collateral to a smart contract. 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. $$(x + r\Delta x)(y - \Delta y) = xy$$ arXiv preprint arXiv:2103.01193, 2021. [5] First be seen in production on a Minecraft server in 2012,[6] CFMMs are a popular DEX architecture. Pact offers a familiar Constant Product Market Maker (CPMM) capability. [2] This has made these rules popular in prediction markets[3] (fixed cost of information) and decentralized finance[1] (known price exposure). Liquidity providers normally earn a fee for providing tokens to the pool. The paper introduces a new type of constant function market maker, the constant power root market marker. (when we want to sell a known amount of tokens) and we can always find the input amount using the $\Delta x$ formula (when Market Makers (MMs) A centralized exchange relies on professional traders or financial institutions, to create multiple bid-ask orders to match the orders of retail traders, or in other words, to provide liquidity. $$\Delta x = \frac{x \Delta y}{r(y - \Delta y)}$$. The converse result was later proven, providing a mechanism for constructing a . 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. saddle.finance. 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!). This AMM enables the creation of AMMs that can have more than. 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. This can be helpful for traders who want to make informed decisions about which assets to buy or sell. 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. Smart contract risk: As with any decentralized platform, constant product AMM DEXs rely on smart contracts to facilitate trades and manage assets. 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