Interest Rate Curve

Overview

Most lending platforms today rely on fixed, governance-controlled interest rate models to set borrowing and lending rates, as well as reserve requirements. These rates are typically determined by internal supply and demand dynamics within the protocol and are largely unaffected by external risk factors or specific characteristics of the deposited assets in the broader market.

Interest rates depend on the utilization (U) of an asset. When U is low, it indicates a surplus in supply and low demand for borrowing. As U approaches 100%, both supply and borrow rates rise, which:

• Encourages lenders to provide more liquidity to the market.

• Encourages borrowers to repay their debt.

$$U=\dfrac{Total Borrow}{TotalLiquidity}$$

Borrow Interest Rate

The current borrowing rate It,​ is defined by the current utilization rate, U t, ​and the discrete function 𝑓 ( 𝑈 𝑖 ) → 𝐼 𝑖 f(U i ​ )→I i ​ , which maps utilization to the borrowing rate at specific knot points.

$$I1=\dfrac{APY-MarginRate}{U1-Uo}(Ut-Uo) ; {0 < Ut <= U1}$$

$$I2=I1+\dfrac{APY-I1}{U2-U1}(Ut-U1) ; {U1<Ut<=U2}$$

$$I3=I2+\dfrac{Ut-U2}{1-U2}(Imax-I2) ; {U2<Ut<100}$$

Where:

It : Current borrow interest rate

APY: Yield of the underlying collateral that is fed in by the oracle to allow the borrowing rate to be adjusted based on the underlying staking yield.

MarginRate: The amount subtracted from the APY to determine the optimal utilization rate

Ut: Current utilization rate

Imax = 100%

Liquidation penalty = 5%

LTV = 93.4%

$$Leverage = \dfrac {1}{1-LTV}=15$$

Liquidation threshold = 96%

Supply Interest Rate

$$S=Ut*It(1-Rt)$$

Where

Rt: Reserve Factor

Curve Example

Interest Rate Curve Example