Interest Rate Model

Introduction

JustLend DAO's interest rate model aims to maximize the utilization of assets while effectively managing liquidity risks. Therefore, the parameter utilization rate $U$ of each market is particularly important, as it reflects the true situation of the available assets in each market. As the utilization rate approaches 100%, assets become scarce, making borrowing impossible. Meanwhile, suppliers may be unable to withdraw their liquidity due to the lack of available assets. The formula of the utilization $U$ is defined as:

$$U \ = Total\ Borrows \ /\ Total\ Supply$$

To calibrate the interest rate model around an optimal utilization rate which reflects the real conditions, JustLend DAO provides variable interest rates for markets through two distinct interest models:

• WhitePaperInterestRateModel:a simple interest rate model where the borrowing rate is directly tied to the utilization rate.

• JumpRateModelV2:operates differently, as the interest rate jumps to a higher tier when the utilization rate surpasses a certain threshold.

Whitepaper Rate Model

The Whitepaper Rate Model is straightforward, as the borrowing rate is directly proportional to the utilization. The interest rate is defined as below.

Borrow Rate:

$$borrow\_rate (u) \ = \ a * u \ + \ b$$

where the borrow utilization rate u is defined as:

$$u \ = borrows \ /\ (cash +borrows - reserves)$$

• borrows: the total amount borrowed in the market, denominated in the underlying asset, excluding bad debts.

• cash: the total amount of the underlying asset held by the market at a specific time.

• reserves: the amount of the underlying asset held by the market that is not accessible to borrowers or suppliers, as it is reserved for purposes outlined in the protocol's tokenomics.

Supply Rate:

$$supply\_rate (u) \ = \ borrow\_rate (u)\ *\ u \ * \ (1\ - \ reserve\_factor )$$

Model Parameters

• a: variable interest rate slope.

• b: base rate per block (baseRatePerYear / blocksPerYear).

• reserve_factor: portion of interest income extracted from the protocol.

Jump Rate Model

The Jump Rate Model is quite different with the Whitepaper Rate Model, where the interest rate jumps to a higher tier when the utilization rate exceeds $u_{optimal}$. The interest rate is defined as below.

Borrow Rate

$if \ \ u < knik:$

$$borrow\_rate (u) \ = \ a_{ 1} \ * \ u \ + \ b$$

$if \ \ u >= knik:$

$$borrow\_rate (u) \ = \ a_{ 1} \ * \ kink \ + \ a_{2} \ * \ (u\ - \ kink) \ + \ b$$

where the borrow utilization rate u is defined as:

$$u \ = \ (borrows )\ /\ (cash +borrows -reserves)$$

• borrows: the total amount borrowed in the market, denominated in the underlying asset, excluding bad debts.

• cash: the total amount of the underlying asset held by the market at a specific time.

• reserves: the amount of the underlying asset held by the market that is not accessible to borrowers or suppliers, as it is reserved for purposes outlined in the protocol's tokenomics.

Supply Rate

$$supply\_rate (u) \ = \ borrow\_rate (u)\ *\ u \ * \ (1\ - \ reserve\_factor )$$

Model Parameters

• a1: variable interest rate slope1.

• a2: variable interest rate slope2.

• b: base rate per block (baseRatePerYear / blocksPerYear).

• kink: the utilization point at which the jump multiplier is applied, and the variable interest rate slope shifts from slope1 to slope2.

• reserve_factor: portion of interest income extracted from the protocol.