CPMM
Constant Product AMM (CPMM)
Introduction
The Constant Product Market Maker (CPMM) is one of the simplest and most widely used automated market maker models. It operates based on a mathematical invariant:
x * y = k
Here, x and y are the reserve balances of two assets (e.g., BTC and Runes), and k is a constant. Each trade alters the reserve ratios but maintains the constant k, resulting in a continuous price curve. This model is ideal for enabling permissionless swaps without order books.
Benefits
Simplicity: Easy to implement and understand.
Always Liquid: The pool always has a price for traders.
Resilience: Stable and predictable behavior under normal conditions.
Limitations
Low Capital Efficiency: Liquidity is spread across all prices.
High Slippage: Particularly for large trades.
No Range Customization: Liquidity providers cannot optimize for specific market ranges.
Example Scenario
Assume a BTC/Runes pool with the following initial state:
1000 BTC
100,000 Runes
A user sells 50 BTC:
Compute the constant:
k = 1000 * 100,000 = 100,000,000After the trade, the pool has 1050 BTC. To maintain
k, the new Runes balance becomes100,000,000 / 1050 ≈ 95,238.10The trader receives
100,000 - 95,238.10 = 4,761.90 RunesAverage execution price:
4,761.90 / 50 ≈ 95.24 Runes per BTCSlippage:
(100 - 95.24) / 100 ≈ 4.76%
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