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How Do Automated Market Makers (AMMs) Work?

AMMs are smart contract systems used by decentralized exchanges (DEXs) to create liquidity pools and determine asset prices algorithmically, rather than using a traditional order book. They rely on a constant product formula (e.g.

$x y = k$) to maintain the relationship between the quantities of two tokens in a pool. Liquidity providers deposit assets and earn fees from trades.

How Do Automated Market Makers (AMMs) in Options Trading Handle Liquidity Risk?
How Do Automated Market Makers (AMMs) Utilize Smart Contracts?
How Do Automated Market Makers (AMMs) Work for Options Contracts?
How Do Automated Market Makers (AMMs) in DeFi Replace Traditional Market Makers?