Interest Rate Model

Overview

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: Whitepaper Rate Model and Jump Rate Model. Each market operates under one of these models with predefined risk parameters upon the market's establishment.

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.

Main parameters of the JustLend DAO markets (as of Jul 17, 2023)

Market	Uₒₚₜᵢₘₐₗ	Base	Slope 1	Slope 2
ETH	-	2.00%	-	32.00%
sTRX	80.00%	2.00%	25.00%	200.00%
TRX	80.00%	2.00%	25.00%	200.00%
USDT	80.00%	0.00%	5.00%	26.80%
USDJ	80.00%	0.00%	5.00%	26.80%
WIN	80.00%	2.00%	32.00%	112.00%
BTC	-	2.00%	-	32.00%
JST	80.00%	2.00%	32.00%	112.00%
WBTT	80.00%	2.00%	32.00%	112.00%
ETHOLD	-	2.00%	-	32.00%
TUSD	80.00%	0.00%	5.00%	26.80%
NFT	80.00%	2.00%	32.00%	112.00%
SUN	45.00%	5.00%	55.00%	275.00%
USDC	80.00%	0.00%	5.00%	26.80%
BUSD	80.00%	0.00%	5.00%	26.80%
BTT	80.00%	2.00%	32.00%	112.00%
USDD	50.00%	1.00%	25.00%	200.00%

Interest Rate Parameters Change History

As market conditions evolve, so do associated risks. JustLend DAO will consistently monitor the utilization rate of each market and promptly adjust interest rate parameters to ensure sustained liquidity in each market. This proactive approach aims to mitigate risks stemming from changing market conditions.

Below is a record of JustLend DAO’s adjusted interest rate Parameters.

Date	Market	Uₒₚₜᵢₘₐₗ	Base	Slope1	Slope2
14 Jul 2023	ETH	-	2.00%	-	32.00%
26 Jun 2023	sTRX	80.00%	2.00%	25.00%	200.00%
22 Jan 2023	USDC	80.00%	0.00%	5.00%	26.80%
22 Jan 2023	BUSD	80.00%	0.00%	5.00%	26.80%
26 Dec 2022	TRX	80.00%	2.00%	25.00%	200.00%
30 Aug 2022	USDC	90.00%	0.00%	5.00%	20.00%
2 Aug 2022	TRX	80.00%	2.00%	30.00%	300.00%
2 Aug 2022	USDD	50.00%	1.00%	25.00%	200.00%
28 Jun 2022	TRX	40.00%	2.00%	20.00%	300.00%
28 Jun 2022	USDD	5.00%	1.00%	20.00%	200.00%
27 Jun 2022	TRX	80.00%	2.00%	25.00%	150.00%
27 Jun 2022	USDD	30.00%	0.00%	5.00%	120.00%