How does the Constant Product Market Maker (CPMM) work? $$r\Delta x = \frac{xy}{y - \Delta y} - x$$ What he didnt foresee, however, was the development of various approaches to AMMs. 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. xy = k. means that the price is determined based on the constant factor k. 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. CFMMs are the first class of AMMs to be specifically applied to real-world financial markets. And this is where we need to bring the demand part back. $$y - \Delta y = \frac{xy}{x + r\Delta x}$$ 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. However, AMMs have a different approach to trading assets. So in the next part, well see how the mathematics This implies a price of 1 ETH = 100 DAI. plotting them on the graph. You need to enable Javascript to view this site properly. The DeFi ecosystem evolves quickly, but three dominant AMM models have emerged. We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). 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. arxiv: 1911.03380 [q-fin.TR] Google Scholar; Jun Aoyagi and Yuki Ito. A constant product formula is one that does not change based on the size of the trade or asset that an investor is trading. 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 RR remains equal to the constant k. money markets, he emphasized that AMMs should not be the only available option for decentralized trading. Token prices are simply relations of reserves: $$P_x = \frac{y}{x}, \quad P_y=\frac{x}{y}$$. "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. Dont be scared by the long name! This loss occurs when the market-wide price of tokens inside an AMM diverges in any direction. While this function produces zero slippage, it does not provide infinite liquidity and thus is likely unfit as a standalone implementation for a decentralized exchange use-case. To build a better intuition of how it works, try making up different scenarios and Minting: Minting refers to the process of creating a new asset or increasing the supply of an existing asset. (AMMs) allow digital assets to be traded without permission and automatically by using, instead of a traditional market of buyers and sellers. a - Number of Tokens of A the trader has . AMM users supply liquidity pools with crypto tokens, whose prices are determined by a constant mathematical formula. Visually, the prices of tokens in an AMM pool follow a curve determined by the formula. . This formula has the desirable property that larger trades (relative to reserves) execute at exponentially worse rates than smaller ones. 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. 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. If 1 ETH costs 1000 USDC, then 1 USDC arxiv: 2012.08040 [q-fin.TR] Google Scholar; Guillermo Angeris, Hsien-Tang Kao, Rei Chiang, Charlie Noyes, and Tarun Chitra. This was pioneered by Unisocks, which created tokens that entitled holders to a physical pair of limited edition socks. The constant formula is a unique component of AMMs it determines how the different AMMs function. Constant Product Market Makers. (the token they want to buy). ETH/BTC). As a result, market makers act as buyers and sellers of last resort. 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. 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. Copyright 2023 Gemini Trust Company, LLC. $$r\Delta x = \frac{x \Delta y}{y - \Delta y}$$ 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 Automated market makers (AMMs) are algorithmic agents that perform those functions and, as a result, provide liquidity in electronic markets. 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. Shell Protocol has similar goals but takes a different approach. 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 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. On this Wikipedia the language links are at the top of the page across from the article title. Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. 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. Broadly speaking, market makers (MM) provide liquidity to the exchange they operate in, and they set "buy" and "sell" quotes for each asset. These AMMs set the prices of assets on a DEX. From this, it is observed that when a user places an order of tokens Get started. This also holds true for AMMs. Connect the world's APIs to Web3 with Chainlink Functions. It is also common to hear the term bonding curve when talking about CFMMs but it is incorrect to do so. Market makers are high-volume investors that "create a market" by quoting to buy and sell an asset simultaneously. 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. The price of tokens in the AMM before adding the liquidity = X/Y. $$-\Delta y = \frac{- y r \Delta x}{x + r\Delta x}$$ A crowdfunded CFMM is a CFMM which makes markets using assets deposited by many different users. 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. This incentivises and rewards LPs proportionally to their ownership percentage of the pool. 2019. The secret ingredient of AMMs is a simple mathematical formula that can take many forms. When we add liquidity it is important to note that there should be no price change before and after adding liquidity. Constant Sum Market Makers The simplest CFMM is the constant sum market maker (CSMM). reserves. Path dependence, in a nutshell, means that history matters. Uniswap went live in November 2018 and epitomized the first automated market maker in the ethereum ecosystem, a model that then became ubiquitous and sparked a number of Uniswap clones (SushiSwap, PankakeSwap, MoonSwap). 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. However, users holding an open position in a synthetic asset are at risk of having their collateral liquidated if the price moves against them.. And when demand is low, the price is also lower. 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. 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. 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. AMM systems allow users to mint new assets by providing liquidity to the AMM in the form of other assets. how it works. The converse result was later proven, providing a mechanism for constructing a . Keywords: Automatic market makers, market microstructure. The first type of CFMM to emerge was the constant product market maker (CPMM), which was popularized by the first AMM-based DEX, Bancor. 1.0.0. . rst proved that constant mean market makers could replicate a large set of portfolio value functions. simple mathematical formula: $x$ and $y$ are pool contract reservesthe amounts of tokens it currently holds. More detailed . Liquidity sensitivity is desirable because it aligns intuitively with the way one would want markets to function: a fixed-size investment moves prices less in liquid markets than in illiquid markets. However, the actual price of a trade 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. Conversely, the price of BTC goes down as there is more BTC in the pool. real estate). Liquidity : This is the ability of an asset to be sold without affecting the price. 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. tokens that the pool is holding. 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. 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. V And its the slope of the tangent line at 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. 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. 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. Users trade against the smart contract (pooled assets) as opposed to directly with a counterparty as in order book exchanges. 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. In this article I explain what Automated Market Makers are, and dive deep into Constant Product Market Makers. Even though Uniswap doesnt calculate trade prices, we can still see them on the curve. As I mentioned in the previous section, there are different approaches to building AMM. 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 Please visit our Cryptopedia Site Policy to learn more. For example, a liquidity pool could hold ten million dollars of ETH and ten million dollars of USDC. 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. 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. This AMM enables the creation of AMMs that can have more than. Available at SSRN 3808755, 2021. As we will see many times in this book, this simple requirement is the core algorithm of how 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. Concluding from the law of supply and demand, high demand increases the priceand this is a property we need to have Because of this matching process, there is the possibility that some orders may take a while to get filled, if ever. 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. This product remains constant during the token swap process such that for time t+1. 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