Interest Rate Model

Utilization Rate	Borrow Rate	Deposit Rate
1.00%	15.25%	0.11%
5.00%	16.23%	0.57%
10.00%	17.46%	1.22%
15.00%	18.69%	1.96%
20.00%	19.92%	2.79%
25.00%	21.15%	3.70%
30.00%	22.38%	4.70%
35.00%	23.62%	5.79%
40.00%	24.85%	6.96%
45.00%	26.08%	8.22%
50.00%	27.31%	9.56%
55.00%	28.54%	10.99%
60.00%	29.77%	12.50%
65.00%	31.00%	14.11%
70.00%	59.57%	29.19%
75.00%	88.14%	46.27%
80.00%	116.71%	65.36%
85.00%	145.29%	86.45%
90.00%	173.86%	109.53%
95.00%	202.43%	134.62%
100.00%	231.00%	161.70%

Borrow Interest Rate

MetaFire’s interest rate algorithm is calibrated to manage liquidity risk and optimize utilization. The borrow interest rates are derived from the Utilization Rate .

Uis an indicator of the availability of capital within the pool. The interest rate model manages liquidity risk in the protocol through user incentives to support liquidity:

• When capital is available: low interest rates to encourage borrowing.

• When capital is scarce: high interest rates to encourage repayments of debt and additional supplying.

Interest Rate Model

Liquidity risk materializes when utilization is high, and this becomes more problematic as $U$ gets closer to 100%. To tailor the model to this constraint, the interest rate curve is split in two parts around an optimal utilization rate $U_{optimal}$. Before $U_{optimal}$the slope is small, after it begins rising sharply.

The interest rate$R_t$follows the model:

$if \hspace{1mm} U \leq U_{optimal}: \hspace{1cm} R_t = R_0 + \frac{U_t}{U_{optimal}} R_{slope1}$

$if \hspace{1mm} U > U_{optimal}: \hspace{1cm} R_t = R_0 + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}}R_{slope2}$

The resulting actual borrow rate is as follows:

$Actual APY = (1+Theoretical APY/secsperyear)^{secsperyear}-1$

• When $U \leq U_{optimal}$ the borrow interest rates increase slowly with utilization
• When $U > U_{optimal}$ the borrow interest rates increase sharply with utilization to above 50% APY if the liquidity is fully utilized.

Deposit Interest Rate

The borrow interest rates paid are distributed as yield for mToken holders who have supplied to the protocol, excluding a share of yields sent to the ecosystem reserve defined by the reserve factor. This interest rate is generated on the asset that is borrowed out then shared among all the liquidity providers.

$D_b = TotalDeposit * B_r * U / \displaystyle\sum_{i=1}^4C_i*A_i$

• $D_b$ the base deposit rate
• $B_r$ the borrow rate
• $U$ the utilization ratio
• $C$ the distributing ratio coefficient
• $A$ the amount of deposit of a specific period