The beautiful math behind Curve AMMs series part 3, this time diving into LLAMMA, Curve’s lending–liquidation AMM.

TL;DR: Curve’s LLAMMA is a new AMM-based liquidation engine for crvUSD that replaces harsh, one-time liquidations with continuous soft liquidation. Collateral is split into price “bands,” and as the oracle price moves, LLAMMA automatically and gradually sells collateral when price drops and buys it back when it rises. It uses virtual balances (f, g) and a hyper-reactive price curve so the AMM price always moves faster than the oracle, creating arbitrage incentives that keep each loan safely rebalanced. The result: smoother liquidations, fewer liquidation cascades, and a mathematically driven lending system where collateral is constantly adjusted instead of wiped out all at once.

Top comment by @Danicjade

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