Borrow Rate

Interest rates play a vital role in balancing deposit reserves and fund utilization rates and help maintain a balanced and efficient utilization of funds within the ecosystem.

Fund Utilization Rate

$$U = \frac{Total_{borrowed}}{Total_{supplied}}$$

We promote borrowing when there is an excess of funds and slow growth interest rates, while increasing loan rates during funding shortages to encourage repayment and maintain liquidity.

TREND CHART

This mechanism ensures a balanced and efficient use of funds in the ecosystem. There are two types of borrowing interest rates: variable and stable. However, the optimal fund utilization rate position is specific to each token pool.

Variable Interest Rate

1. Rate Performance During Funds Redundancy

• Under the optimal fund utilization rate

• Gradually increasing interest rates

$$R_t = R_{0} + \frac{U_t}{U_{optimal}} \times R_{slope1}$$

• $R_{0}$Initial interest rate, which is a preset parameter
• $R_{slope1}$、$R_{slope2}$ is to adjust the slope of the function, are preset parameters
• $U_t$ Utilization rate of current liquidity pool
• $U_{optimal}$Optimal utilization rate -is to adjust the slope of the function, are preset parameters

2. Rate Performance During Insufficient liquidity

• Exceeding the optimal fund utilization rate

• Steep rise in interest rate cost

$$R_t = R_{0} + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}} \times R_{slope2}$$

Stable Interest Rate

• The stable interest rate for borrowing is generally higher than the variable interest rate for the same level of fund utilization.

• Due to the high liquidity volatility, the protocol does not support stable-rate loans for some specific tokens.

• If a user wants to borrow the asset they deposits, the borrowed amount must be greater than the deposited amount. Users must also follow it to switch from variable to stable rates successfully.

• The maximum borrowing amount for a user on a stable-rate loan cannot exceed 25% of the liquidity in the corresponding token pool.

• In extremely exceptional circumstances, the stable interest rate may be disrupted and reset, requiring recalculation.

Stable interest rates can not adapt to relevant changes and lose the capability to adjust for risk. Therefore, we need to proactively mitigate risks.

The Optimal Stable-Rate Loan Ratio refers to the ideal proportion of stable-rate loans within the pool that ensures a balanced and manageable level of liquidity risk.

$$Ratio=\frac{Stable\ Rate\ Liabilities} {Total\ Liability }$$

• $R_{0}$Initial interest rate, which is a preset parameter.
• $R_{slope1}$、$R_{slope2}$ is to adjust the slope of the function, are preset parameters.
• $U_t$ Utilization rate of current liquidity pool.
• $U_{optimal}$Optimal utilization rate -is to adjust the slope of the function, are preset parameters.
• $O_{ratio}$Optimal ratio, which is a preset parameter.

1. Rate Performance During Funds Redundancy

• Under the optimal fund utilization rate

• Gradually increasing interest rates

$$R_{base} = \begin{cases} R_0 + \frac{U_t}{U_{optimal}} \times R_{slope1} &\text{if } U \leq U_{optimal} \\ R_0 + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}} \times R_{slope2} &\text{if } U \gt U_{optimal} \end{cases}$$

2. Rate Performance During Insufficient Liquidity

• Exceeding the optimal fund utilization rate

• Steep rise in interest rate cost

$$R_t = \begin{cases} R_{base} &\text{if } ratio \leq O_{ratio} \\ R_{base} + \frac{ratio - O_{ratio}}{1 - O_{ratio}} \times offset &\text{if } ratio \gt O_{ratio} \end{cases}$$

HopeLend protocol adjusts interest rates by adding an offset weight to the base rate, depending on the deviation of the current ratio from the reasonable ratio.

Stable Rate Reset

The stable interest rate will be reset if the weighted average interest rate based on currently supplied liquid borrowings is less than 90% of the variable loan rate.

$${LR}_t < 0.9\times{Variable\ loan\ late}$$

The relevant reference formula:

$$\bar{R_t} = \frac{variable\ debt}{total\ debt} \times {R_{variable}} + \frac{stable\ debt}{total\ debt} \times {R_{stable}}$$

$${LR}_t = \bar{R_t}{ U_t} \times (1 - Reserve\ Factor)$$

• $U_t$ Utilization rate of current liquidity pool.
• Reserve Factor