A Mathematical Breakdown of How Automated Market Makers Price Assets

About this episode

This episode provides a mathematical breakdown of how Automated Market Makers price assets and discusses related concepts like impermanent loss and liquidity pools.

This story was originally published on HackerNoon at: https://hackernoon.com/a-mathematical-breakdown-of-how-automated-market-makers-price-assets . Learn how AMMs price tokens using x·y=k, how fees accrue, and why impermanent loss hurts LPs. From Uniswap V2 to V3, the math explained clearly. Check more stories related to web3 at: https://hackernoon.com/c/web3 . You can also check exclusive content about #defi , #automated-market-makers , #amm-math , #uniswap-v2 , #concentrated-liquidity , #liquidity-pools , #curve-finance , #crypto-liquidity , and more. This story was written by: @durdana-yembergenova . Learn more about this writer by checking @durdana-yembergenova's about page, and for more stories, please visit hackernoon.com . AMMs use the formula x·y=k to price tokens without an order book. Swaps move reserves along a hyperbola, causing price impact on large trades. A 0.30% fee grows k over time, rewarding liquidity providers. LPs face impermanent loss — always worse than holding when price moves, calculated as IL(r) = 2√r/(1+r) − 1. Uniswap V3 improves capital efficiency via concentrated liquidity ranges, while Curve and Balancer extend the model to stablecoins and…

Topics covered

• Automated Market Makers
• DeFi
• Token Pricing
• Liquidity Pools
• Uniswap
• Impermanent Loss

Keywords

• AMM
• x·y=k
• liquidity providers
• impermanent loss
• Uniswap V3
• concentrated liquidity
• crypto liquidity

Mentioned in this episode

Organizations: HackerNoon, Uniswap, Curve, Balancer

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