Interest Rate Model

The Interest Rate Model (IRM) functions as the protocol's algorithmic central bank. Its primary objective is to balance capital efficiency (maximizing yield for lenders) with liquidity availability (ensuring lenders can withdraw assets).

It achieves this by dynamically adjusting the Base Borrow Rate based on the Utilization Rate of the Liquidity Pool.

The Utilization Curve

The cost of borrowing is a function of demand. As the pool becomes more utilized (more funds borrowed), the interest rate rises to incentivize repayments and attract new deposits.

Gearbox employs a Two-Kink Piecewise Linear Model. This design creates a specific "Optimal Zone" where rates remain stable, preventing volatility during normal market activity while aggressively penalizing over-utilization.

Mathematical Structure

The curve is defined by two utilization thresholds (Kinks), denoted as U_1 and U_2, creating three distinct slope zones:

1. Growth Zone (0% to U_1):

   • Behavior: Rates increase slowly.

   • Intent: Incentivize early borrowing and ramp up utilization to efficient levels.

2. Optimal Zone (U_1 to U_2):

   • Behavior: Rates remain relatively stable or rise moderately.

   • Intent: Create a predictable cost of capital for borrowers while ensuring sufficient yield for lenders. This is the target operating range of the pool.

3. Liquidity Crunch Zone (> U_2):

   • Behavior: Rates spike exponentially (High Slope).

   • Intent: Force immediate deleveraging. When utilization breaches U_2, the cost of capital exceeds market returns, compelling borrowers to close positions and restoring liquidity for lender withdrawals.

Formula

The Borrow Rate R(U) is calculated as:

$$R(U)= \begin{cases} R_{\text{base}} + \dfrac{U}{U_1} R_{\text{slope1}}, & U \le U_1 \\[6pt] R_{\text{base}} + R_{\text{slope1}} + \dfrac{U - U_1}{U_2 - U_1} R_{\text{slope2}}, & U_1 < U \le U_2 \\[6pt] R_{\text{base}} + R_{\text{slope1}} + R_{\text{slope2}} + \dfrac{U - U_2}{1 - U_2} R_{\text{slope3}}, & U > U_2 \end{cases}$$

Where:

• U: Current Utilization Rate (Total Debt / Total Assets).

• R_base: The minimum starting rate (y-intercept).

• R_slope: The rate of change in each zone.

Reference:

• Desmos IRM visualizer

Liquidity Reservation

A critical feature of the Gearbox IRM is the enforcement of Exit Liquidity.

In standard lending protocols, 100% utilization means lenders cannot withdraw their funds until a borrower repays. Gearbox mitigates this risk through Liquidity Reservation.

The Reservation Cap

Curators can configure the market to strictly forbid new borrowing once utilization reaches U_2.

• Mechanism: If isBorrowingMoreU2Forbidden is enabled, any transaction attempting to increase debt beyond the U_2 threshold will revert.

• Result: The remaining liquidity (from U_2 to 100%) is effectively reserved for lender withdrawals. Even in periods of peak demand, a buffer of liquid assets remains available in the pool.

Total Cost of Capital

The Interest Rate Model determines the Base Rate of the pool. The final cost to a borrower includes additional collateral-specific rate.

Learn More

• Asset-specific risk premiums: Borrowers holding specific collateral assets may incur an additional Quota Rate on top of the base rate.

  • Collateral Limits & Specific rates

• Protocol fees: A portion of the interest paid is captured as revenue for the Protocol DAO and the Market Curator.

  • DAO & Curators' business model