Free module · Crypto & decentralized finance

DeFi: AMMs, Liquidity Provision and Lending

Follow reserves, benchmark inventory and test collateral under stress.

constant product · ranges · LP inventory · LVR · lending · liquidation

The building blocks

DeFi contracts automate accounting rules, while prices, liquidity and collateral remain economic risks. Learn the accounting before comparing advertised yields.

Derive the reserve or debt state transition.
Compare outcomes with an explicit benchmark.
Stress price, oracle, fee and execution assumptions.

Lessons in this module

Open the interactive module

Practice and apply

Constant-product swaps with an input fee — Reserves 100 base, 10000 quote; input 10 base; fee .003. Find quote output.
LP inventory after price changes — Invariant 1000000 base×quote and price 400 quote/base. Find base reserve.
LP value versus holding the original tokens — No-fee constant-product pool; final/initial base price ratio 2. Find relative LP minus hold ratio.
Concentrated liquidity and range boundaries — L=100, lower price 1, current 4, upper 9. Find quote inventory.
LVR and the price of stale inventory — Rebalancing value 10030, pool value 10000 before fees, collected fees 40, other costs 8. Find net comparison.
Lending utilization and rate response — Borrowed 80, supplied 100, base .02, low slope .10, kink .7, high slope 1. Find annual borrow rate.
Collateral health factor and correlated shocks — Collateral value 12000, liquidation threshold .8, debt 8000. Find health factor.
Liquidation incentives after execution costs — Repay 1000 USD, bonus .05, sale discount .02, fixed gas/cost 10. Find net profit.

Work through the practice exercises · Quant development tools