Yield OceanISSUE #11 of 34

interest rate models · utilization curves

Liquidity LuVSThe Sandwich Bot

Liquidity Lu saysLending rate models map utilization (borrowed / supplied) to APR — flat below a kink, steep above, pushing utilization back toward the target by repricing borrows.

Lending markets need rate dynamics that keep liquidity. A typical kinked interest rate model has two slopes: gentle below a target kink utilization (e.g., 80%), and steep above. At low utilization, rates are barely above base; above the kink they spike, pushing borrowers to repay and lenders to deposit, restoring liquidity.

The demo computes borrow APR at five utilization levels and shows the slope discontinuity at the kink.

Power-ups you unlock

Utilization U = borrowed / supplied
Kinked model: gentle slope below U_kink, steep above
Above the kink, rates spike to push U back down
Base + slope1·(U/U_kink) for U ≤ U_kink
Base + slope1 + slope2·(U − U_kink)/(1 − U_kink) above

The Sandwich Bot attacks — common mistakes

Setting U_kink so high it never triggers under stress
Forgetting borrow rate and supply rate are coupled via U
Using a linear model for assets with bursty utilization
Ignoring rate spikes during peak demand

Boss battleCompute borrow APR at utilization 20%, 50%, 80%, 90%, and 95% with base=2%, slope1=4%, slope2=75%, kink=80%.

Example code

<!doctype html><html><head><meta charset="utf-8"></head>
<body style="background:#06040d;color:#e6e0ff;font-family:monospace;padding:20px"><pre id="o"></pre>
<script>
const BASE = 0.02, SLOPE1 = 0.04, SLOPE2 = 0.75, KINK = 0.80;
function borrowAPR(u){
  if(u <= KINK) return BASE + (u / KINK) * SLOPE1;
  return BASE + SLOPE1 + ((u - KINK) / (1 - KINK)) * SLOPE2;
}
const rows = [0.20, 0.50, 0.80, 0.90, 0.95].map(u =>
  '  U=' + String(Math.round(u*100)).padStart(3) + '%  → borrow APR ' + (borrowAPR(u)*100).toFixed(2) + '%'
);
document.getElementById('o').textContent = [
  'kinked interest model (base=2%, slope1=4%, slope2=75%, kink=80%):',
  '',
  ...rows,
  '',
  'gentle slope below 80% utilization, steep above to push U back down'
].join('\n');
</script></body></html>

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