CPMM
Constant Product AMM (CPMM)
Mathematical Foundation and Implementation
CPMM implements the fundamental invariant: x × y = k, where x and y represent reserve balances of two assets, and k remains constant across all trading operations.
This model provides predictable, continuous liquidity across all price levels, making it particularly suitable for assets with uncertain price ranges or for liquidity providers seeking simplified position management.
Operational Characteristics
Technical Advantages:
Algorithmic Simplicity: Straightforward implementation with predictable behavior patterns
Continuous Availability: Guaranteed liquidity provision at all price levels without gaps
Operational Resilience: Stable performance under various market conditions and volatility scenarios
Inherent Limitations:
Capital Inefficiency: Uniform distribution across infinite price range results in suboptimal capital utilization
Slippage Impact: Large trades experience significant price impact due to distributed liquidity
Strategy Constraints: No customization options for specific price range optimization
Performance Analysis
Execution Example: Pool State: 1,000 BTC × 100,000 Runes (k = 100,000,000)
For a trade selling 50 BTC:
Post-trade BTC balance: 1,050 BTC
Post-trade Runes balance: 100,000,000 ÷ 1,050 = 95,238.10 Runes
Runes received: 4,761.90 Runes
Average execution price: 95.24 Runes per BTC
Price impact: 4.76%
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