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. The most popular of them is the Constant Function Market Makers (CFMM) [37], which maintain a mathematical invariant (for example, a product of the quantity of assets) during the trade. What he didnt foresee, however, was the development of various approaches to AMMs. Recently, liquidity providers have also been able to earn yield in the form of project tokens through what is known as yield farming.. However, the execution price is 0.666, so we get only 133.333 of token 1! 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. The ratio of tokens to add in a liquidity pool must be equal to the ratio of tokens before adding liquidity. Adding liquidity to a CFMM is simple but comes with some complex financial risks (impermanent loss, short volatility, long volatility/volume correlation, etc.). Since Uniswap pools are separate smart contracts, tokens in a pool are priced in terms of each other. They allow digital assets to be traded in a permissionless and automatic way by using liquidity pools rather than a traditional market of buyers and sellers. Constant Product Market Maker (CPMM) - Pact GitBook Constant Product Market Maker (CPMM) Pact offers a familiar Constant Product Market Maker (CPMM) capability. Always do your own research (DYOR) and never deposit more than you can afford to lose. In other words, in the absence of fees, constant mean markets ensure that the weighted geometric mean of the reserves remains constant. plotting them on the graph. In contrast to regular market makers, AMMs function by using self-executing computer programs, also known as smart contracts. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged: Uniswap, Curve, and Balancer. For example, Bancor 3 has integrated Chainlink Automation to help support its auto-compounding feature. Keywords: Automatic market makers, market microstructure. 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]. One of the most popular models adopted by automated market maker platforms is the constant product market maker (CPMM) model. 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. Impermanent loss is the difference in value over time between depositing tokens in an AMM versus simply holding those tokens in a wallet. This chapter retells the whitepaper of Uniswap V2. 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 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. The above limitations are being overcome by innovative projects with new design patterns, such as hybrid automated market makers, dynamic automated market makers, proactive market makers, and virtual automated market makers. Liquidity providers normally earn a fee for providing tokens to the pool. $$(x + r\Delta x)(y - \Delta y) = xy$$ AMMs democratized cryptocurrency trading by doing away with order books and institutional market makers. it simply prices the trade based on the Constant Product Formula. 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. The structure of the paper is as follows. Learn about the role of oracles, use cases, and more. 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. Conversely, the price of BTC goes down as there is more BTC in the pool. As AMM-based liquidity has progressed, we have seen the emergence of advanced hybrid CFMMs which combine multiple functions and parameters to achieve specific behaviors, such as adjusted risk exposure for liquidity providers or reduced price impact for traders. prices when making a trade: And thats the whole math of Uniswap! 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. An automated market maker (AMM) is a system that automatically facilitates buy and sell orders on a decentralized exchange. A qualified professional should be consulted prior to making financial decisions. Additionally, liquidity provider fees could be based on other factors in addition to liquidity. Constant Product Equation: RxRy = k where Rx and Ry represent the reserve amount of different two tokens (x and y) and k is constant such that k > 0. 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. A constant sum function forms a straight line when plotting two assets, resulting in the equation x+y=k. 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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. 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. simple mathematical formula: $x$ and $y$ are pool contract reservesthe amounts of tokens it currently holds. Liquidity providers normally earn a fee for providing tokens to the pool. $$-\Delta y = \frac{xy - xy - y r \Delta x}{x + r\Delta x}$$ arxiv: 2012.08040 [q-fin.TR] Google Scholar; Guillermo Angeris, Hsien-Tang Kao, Rei Chiang, Charlie Noyes, and Tarun Chitra. [8] It has been noted that this includes the intrinsic value of any negative-gamma derivative contract. 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. As such, most liquidity will never be used by rational traders due to the extreme price impact experienced. Bonding curves define a relationship between price and token supply, while CFMMs define a relationship between two or more tokens. It uses the following functions: Where U(x) could be interpreted as a utility function comprised of a gain function, G(x), and a loss function, F(x); and x is the reserves of each asset. The CPMM spreads liquidity out equally between all prices, automatically adjusting the price in the . 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. Curve and Shell have demonstrated that there exists a design space for constant functions that are tailored for specific types of digital assets. Suggested . This has made these rules popular in prediction markets (fixed cost of . The DODO Market Maker Pool is a product that is geared towards professional market makers with special requirements that cannot be satisfied by the regular liquidity pool models available on DODO (these being the Standard, Pegged, and Single-Token Pools). So in the next part, well see how the mathematics 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. Users supply liquidity pools with tokens and the price of the tokens in the pool is determined by a mathematical formula. XY=K.The best example of a DEX that uses this is Uniswap and Bancor. It can be called a hybrid AMM since it uses elements from both the constant product and constant sum market makers. ( Ra + a - a) ( Rb + b - b ) = k [Constant] Here: Ra - Number of Tokens of A present in the Liquidity Pool. This mechanism ensures that Pact prices always trend toward the market price. real estate). and decentralized finance (DeFi). reserves. 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. This type of AMM will adjust its exchange rates automatically based on demand and supply to maintain that ratio. Under this option, liquidity providers need to supply each token in the pair with an equal or 50:50 value. Lets visualize the constant product function to better understand Liquidity sensitivity for todays CFMMs is limited to price (i.e. pool reserves. What Are Automated Market Makers (AMMs)? 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