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DeFi interest rate model

A DeFi interest rate model maps pool utilization to borrowing and supply rates. Learn how kinked curves, reserve factors, rate accrual, and liquidity risks work.

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For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

A DeFi interest rate model is a set of smart-contract rules that maps a lending market’s utilization to the rates paid by borrowers and, directly or indirectly, earned by suppliers. Its purpose is to price scarce liquidity: when more of a pool is borrowed, the borrow rate generally rises to discourage additional borrowing and encourage repayment or new supply.

Many protocols use a kinked, or two-slope, curve. Rates rise gradually below a target utilization and much faster above it, helping preserve enough liquid assets for withdrawals. The model is market-specific: each asset, deployment, or protocol version may have different parameters and even a different formula.

The interest rate model does not decide whether an account is solvent. Collateral factors, oracle prices, health-factor rules, and liquidation logic perform that job. It also does not guarantee that suppliers can withdraw immediately; withdrawals still depend on available liquidity.

How it works

Let U be utilization and B total borrows. Compound v2 defines U = B / (cash + B - reserves), while Compound III uses U = B / S for total supplied base-asset principal S and returns 0 when supply is zero. Aave’s current strategy derives usage from debt and available liquidity and also accounts for unbacked liquidity. The deployed contract is therefore the authoritative definition.

For a simple kinked borrow curve, let b be the base annualized rate, K the kink, and m1 and m2 the slopes below and above the kink:

  • When U <= K: r_b = b + m1 * U
  • When U > K: r_b = b + m1 * K + m2 * (U - K)

This notation makes the curve continuous at K. Protocol code may parameterize the slopes differently. For example, a slope may represent the full rate increase across a segment rather than a coefficient multiplied directly by utilization. Always read the implementation before reproducing a displayed APR.

In models where the supplier rate is derived from borrower interest, an approximate relationship is r_s = r_b * U * (1 - f), where f is the reserve factor retained by the protocol. This is not universal. Compound III, for example, configures separate supply and borrow curves. Token incentives are also separate from the underlying-asset interest rate and can make a displayed yield differ from the model rate.

Interest usually accrues through supply and borrow indexes. A quoted rate is therefore a current annualized rate, not a fixed promise for the next year. APR and APY can also differ because APY assumes a compounding convention; interfaces may annualize per-second or per-block rates and may update at different times.

Example

Assume a model defines b = 2%, K = 80%, m1 = 5%, and m2 = 80%, with all rates annualized. At U = 70%, the borrow rate is 2% + 5% * 70% = 5.5%.

If utilization rises to U = 95%, the above-kink formula gives 2% + 5% * 80% + 80% * (95% - 80%) = 18%. The steep second slope makes the last 15 percentage points of utilization much more expensive.

Under a derived-supply model with f = 10%, the corresponding supplier rate would be approximately 18% * 95% * (1 - 10%) = 15.39%. That figure excludes token incentives and assumes the stated rates, utilization, and reserve factor do not change. Under a protocol with a separate supply curve, this calculation would not apply.

Risks

  • Liquidity risk: Near U = 100%, little cash may remain for withdrawals. A high rate is an incentive to restore liquidity, not proof that liquidity will arrive.
  • Variable-rate risk: Borrow costs can rise quickly after the kink. A position that is affordable at entry can become expensive before the borrower can repay or refinance.
  • Parameter and governance risk: Authorized governance can change the base rate, kink, slopes, reserve factor, or the strategy contract. Historical rates do not define future rates.
  • Implementation risk: Rounding, stale indexes, unusual token behavior, or a faulty upgrade can make actual accrual differ from a simplified spreadsheet model.
  • Display risk: Interfaces may mix APR, APY, incentive emissions, or cached data. Verify units, scaling, compounding assumptions, and the contract address.
  • Protocol risk: The rate model does not remove smart-contract, oracle, collateral, liquidation, stablecoin, or governance failures.

Common misconceptions

Myth 1: A high utilization rate is always good

High utilization means capital is being used, but it also means less liquidity is available for withdrawals. Above the kink, the protocol is usually signaling scarcity rather than ideal conditions.

Myth 2: The displayed supply APY is paid directly by borrowers

Some models derive supplier interest from borrower payments after reserves, while others use a separate supply curve. Incentive tokens may add another yield source. The interface total must be decomposed before comparing markets.

Myth 3: A current APR is locked in for one year

Utilization and governance parameters can change, so variable rates can move from one block or accrual interval to the next. Annualization describes the current rate under a convention; it is not a forward guarantee.

Myth 4: The same utilization implies the same rate everywhere

Two markets can have the same U but different base rates, kinks, slopes, reserve factors, and formulas. Compare the deployed model and parameters, not utilization alone.

Sources

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