Interest Rate Model

Description

Sake Finance employs a variable interest rate model to manage liquidity risk and optimize utilization.

The borrow interest rate follows a piecewise linear function based on the utilisation rate. The interest rate increases slowly until the optimal utilization rate and then more rapidly at high utilization, effectively balancing supply and demand in the protocol.

Borrow Rate Formula

$$\text{If } U \leq U_{\text{optimal}}: R_t = R_0 + \left(\frac{U_t}{U_{\text{optimal}}}\right) \times R_{\text{slope1}}$$

$$\text{If } U > U_{\text{optimal}}: R_t = R_0 + R_{\text{slope1}} + \left(\frac{U_t - U_{\text{optimal}}}{1 - U_{\text{optimal}}}\right) \times R_{\text{slope2}}$$

Where:

• $U$ = Utilisation Rate

• $U_{\text{optimal}}$ = Optimal utilization point

• $R_t$ = Interest rate at time t

• $R_0$ = The starting interest rate

• $U_t$ = Utilization rate at time t

• $R_{\text{slope1}}$ = How fast rates rise under normal conditions

• $R_{\text{slope2}}$ = How fast rates rise when borrowing is high

Different models use varied parameters to encourage lending and prevent over-borrowing, tailoring to specific market needs and risk profiles.

Supply Rate

The supply rate is the interest earned by users who provide liquidity to Sake Finance. It's calculated based on the interest paid by borrowers, minus a portion set aside for the protocol's reserve.

The supply APY, $S_t$, is:

$$S_t = U_t \cdot R_t \cdot(1 - RF)$$

Where:

• $S_t$ = Supply interest rate
• $U_t$ = Utilization ratio
• $R_t$ = Borrow interest rate
• $RF$ = Reserve factor

The reserve factor is the percent of protocol interest that goes to the Sake Ecosystem Reserve. Each Sake market has a collector contract which stores the revenue from the reserve factor.

Main Interest Rate Model Parameters

Interest rate model	U_optimal	R_0	R_slope1	R_slope2
Variable	45%	0%	7%	300%
Stable one	90%	0%	4%	60%
Stable two (for high liquidity stablecoins)	80%	0%	4%	70%

Supported Assets

Variable Interest Rate Model

• WBTC

• WETH

Stable One Interest Rate Model

• DAI

Stable Two Interest Rate Model

• USDT

• USDC