Free lesson · DeFi models

Lending utilization and rate response

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A lending pool becomes less liquid when more supplied funds are borrowed. A rate curve can make additional borrowing more expensive near a utilization threshold.

Use a simplified kinked model: a base annual rate plus one slope below a utilization kink and another above it. Rates are decimal annualized fractions, not per-block rates.

Utilization definitions differ by protocol when reserves, unbacked assets or special debt modes exist. Supply yield also differs from borrow rate because only borrowed capital earns interest and part may go to reserves.

Apply it in a strategy

• Stress carry financing and withdrawal liquidity under rising lending-pool utilization.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: A protocol can define slope parameters differently, and variable rates can change before a trade unwinds.

Research deliverable

Build and explain a lending utilization and rate response worksheet. Stress carry financing and withdrawal liquidity under rising lending-pool utilization.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def borrow_rate(borrowed,supplied,base,slope1,slope2,kink):
    if supplied<=0 or not 0<=borrowed<=supplied or not 0<kink<1 or min(base,slope1,slope2)<0: raise ValueError("Invalid lending inputs")
    u=borrowed/supplied
    return u,base+slope1*min(u,kink)+slope2*max(0,u-kink)

print(borrow_rate(80,100,.02,.10,1,.7))