Pendle AMM
Standard AMMs (like Uniswap) don't account for time. Pendle built a custom AMM where the pricing curve automatically shifts as maturity approaches, ensuring PT prices converge to 1.0 at expiry. The AMM concentrates liquidity around the implied yield rate, not the token price.
⏱️ Time Decay Visualization
PT Price
0.9756
YT Price
0.0244
Time to Maturity
180 days
Curve Concentration
Moderate
🔬 How Pendle's AMM Differs from Uniswap
🦄 Uniswap (x·y=k)
- Static curve — doesn't change over time
- Liquidity spread evenly across all prices
- No concept of maturity or convergence
- Great for volatile pair trading
⏳ Pendle AMM
- Curve shifts automatically as time passes
- Concentrates liquidity around implied yield
- PT guaranteed to converge to 1.0 at maturity
- Minimizes IL for LP providers near expiry
📐 The Math: Yield Space Invariant
x^(1-t) + y^(1-t) = k
Where t is the time-to-maturity factor (0 to 1). As t → 0 (approaching maturity), the curve flattens and behaves like a stableswap (low slippage near 1:1). At t = 1 (far from maturity), it behaves more like a constant-product curve. This elegantly handles the PT→1.0 convergence.