Interest Rate Model

What Is an Interest Rate Model?

An interest rate model is a formula embedded in a smart contract that determines how much borrowers pay and how much lenders earn on a DeFi lending protocol. Rather than relying on a central committee or fixed schedule, the model makes rates fully algorithmic: they move up or down each block in response to real-time supply and demand.

The core input to the model is the utilization rate: the ratio of total borrows to total deposits in a given market. When utilization is low, capital is sitting idle and the protocol lowers rates to attract borrowers. When utilization is high, depositors might struggle to withdraw, so the protocol raises rates to discourage new borrows and incentivize fresh deposits.

Protocols such as Aave and Compound popularized this approach starting in 2020. Today, nearly every overcollateralized lending protocol uses some variant of a utilization-based interest rate model, though the specific curve shape and parameters vary significantly across platforms and asset types.

How It Works

The standard interest rate model used by Aave V3 and similar protocols is a piecewise linear function with two segments separated by a kink point. The kink occurs at a target utilization level called the optimal utilization (U_opt).

The Two-Slope Formula

The borrow rate R at any given utilization U is calculated as follows:

When U ≤ U_opt (below optimal utilization):
  R = R_base + R_slope1 × (U / U_opt)

When U > U_opt (above optimal utilization):
  R = R_base + R_slope1 + R_slope2 × (U - U_opt) / (1 - U_opt)

Below the optimal point, the rate increases at a moderate pace governed by slope 1. Above the optimal point, slope 2 takes over, and rates climb rapidly toward the protocol's maximum. The transition at U_opt creates the visible "kink" in the rate curve.

Key Parameters

Every interest rate model is defined by four governance-controlled parameters:

These parameters are set per reserve (per market). A stablecoin pool might use a 90% optimal utilization because stablecoin supply and demand is relatively predictable, while a volatile long-tail asset might use 45% to maintain a larger withdrawal buffer.

Supply Rate Derivation

In Aave V3, lenders earn a share of the borrow interest proportional to the current utilization, reduced by a reserve factor that the protocol retains as revenue:

Supply Rate = Borrow Rate × Utilization × (1 - Reserve Factor)

If the borrow rate is 5%, utilization is 80%, and the reserve factor is 10%, then the supply rate works out to 5% × 0.80 × 0.90 = 3.6% APY. This mechanic aligns lender returns with actual protocol usage.

Compound V3 (Comet) takes a different approach: it defines separate supply-side parameters (its own base rate, slope, and kink), giving governance independent control over what lenders earn versus what borrowers pay.

Solidity Implementation

At the contract level, rates are typically computed per second and scaled by 10¹⁸ for precision. A simplified Solidity implementation of the kinked model looks like this:

function getBorrowRate(uint256 utilization) public view returns (uint256) {
    if (utilization <= optimalUtilization) {
        return baseRate + (slope1 * utilization) / optimalUtilization;
    } else {
        uint256 excessUtilization = utilization - optimalUtilization;
        uint256 maxExcess = 1e18 - optimalUtilization;
        return baseRate + slope1 + (slope2 * excessUtilization) / maxExcess;
    }
}

The protocol calls this function whenever a borrow, repayment, deposit, or withdrawal changes the utilization. Rates update in real time with every transaction, meaning there is no lag between market conditions and the rate a borrower pays.

Model Variants

Linear Model

The simplest approach: a single straight line from the base rate at 0% utilization to a maximum rate at 100%. Linear models are easy to reason about but lack the safety mechanism of a steep zone near full utilization, making depositor withdrawals risky during demand spikes.

Kinked (Two-Slope) Model

The industry standard, used by Aave V3, Compound V3, and most forks. Two linear segments joined at the optimal utilization point create a "kink" that discourages utilization from exceeding the target. The steep upper slope acts as a built-in circuit breaker: if too much capital is borrowed, rates spike to incentivize repayments and fresh deposits.

Adaptive (Dynamic) Models

Newer protocols experiment with models that automatically adjust their parameters over time rather than relying solely on governance votes. Morpho, for example, adjusts a scaling factor that shifts the entire curve up or down based on whether utilization is persistently above or below target. Academic research has proposed control-theory approaches (including PID controllers) that could respond more quickly to market shocks. These remain largely experimental, and most major protocols still use the static kinked model with governance-driven parameter updates.

Why Different Assets Need Different Curves

Not all assets behave the same way. A protocol's risk team calibrates each market's interest rate model to match that asset's risk profile:

• Stablecoins (USDC, USDT): optimal utilization around 90%: 93%, low slope 1, moderate slope 2. Stable demand patterns allow high utilization without excessive withdrawal risk.
• Blue-chip volatile assets (ETH, BTC): optimal utilization around 70%: 80%, moderate slopes. Price volatility means liquidations can cause sudden repayment waves, so the protocol keeps a larger idle buffer.
• Long-tail assets (low-cap tokens): optimal utilization around 45%: 65%, aggressive slope 2. Thin liquidity and higher manipulation risk justify conservative parameters and a wide withdrawal margin.

Risk teams at organizations like Gauntlet, Chaos Labs, and LlamaRisk continuously model these parameters and submit governance proposals to adjust them as market conditions change.

Use Cases

Overcollateralized Lending

The primary use case: protocols like Aave, Compound, and Spark (MakerDAO) use interest rate models to balance supply and demand across dozens of asset markets simultaneously. Borrowers post collateral exceeding their loan value, and the interest rate model ensures that depositors are fairly compensated based on how much of their capital is actively deployed. For a deeper look at how these protocols compare, see the stablecoin-backed lending platforms analysis.

Stablecoin Minting

Some stablecoin issuers (such as MakerDAO with DAI) use interest rate models to set the cost of minting new stablecoins against collateral. The "stability fee" functions similarly to a borrow rate and is adjusted to maintain the dollar peg. When demand for DAI is high, the fee rises to slow issuance; when demand drops, the fee falls to encourage minting. Learn more about how overcollateralization supports these systems.

Yield Strategy Optimization

Yield aggregators and automated vaults monitor interest rate curves across multiple protocols to find the best supply rates. Because the shape of the curve is deterministic and on-chain, smart contracts can calculate expected returns before committing capital. The transparency of the model is what makes DeFi yield optimization programmable and composable.

Flash Loan Arbitrage

When a rate model pushes borrow costs high on one protocol but rates remain low on another, arbitrageurs can use flash loans to rebalance positions across protocols in a single transaction, profiting from the rate differential.

Risks and Considerations

Governance Risk

Because parameters are set through governance token voting, a poorly calibrated proposal could set slope 2 too low (failing to deter excessive borrowing) or too high (making the protocol uncompetitive). Whale voters or compromised governance processes could manipulate rate parameters for profit.

Liquidity Crunch

Even with a steep slope 2, extreme market events can push utilization to 100% before rates have time to attract new deposits. During the March 2023 USDC depeg, several lending markets hit near-100% utilization, temporarily preventing depositor withdrawals. The interest rate model is a soft incentive mechanism, not a hard guarantee of liquidity.

Oracle and Liquidation Interaction

Interest rate models do not operate in isolation. When oracle price feeds trigger liquidations, borrowers are forced to repay, which rapidly changes utilization and therefore rates. A sudden cascade of liquidations can cause rates to swing dramatically within a single block. Protocols must design their rate model alongside their health factor and liquidation mechanics to avoid destabilizing feedback loops.

Model Rigidity

The static kinked model cannot adapt to changing market conditions without a governance vote, which can take days. If external lending rates shift rapidly (for example, when the Federal Reserve changes its benchmark rate), DeFi rates may be slow to follow. Adaptive models attempt to solve this, but introduce their own risks: an automated adjustment mechanism could be manipulated by strategic actors who temporarily push utilization to extreme levels to influence future rate parameters.

Interest Rate Models and Stablecoin Lending

Interest rate models are especially important for stablecoin markets, where the spread between borrow and supply rates directly affects the cost of dollar-denominated lending. For platforms building on Bitcoin layer 2 networks like Spark, understanding how these models price risk is essential for integrating with or competing against Ethereum-based lending markets. The stablecoin yield landscape provides a broader view of how rates compare across the ecosystem.

This glossary entry is for informational purposes only and does not constitute financial or investment advice. Always do your own research before using any protocol or technology.