Borrowing Interest Rate Model

The Likwid Protocol uses a tiered borrowing rate curve configured through marginState in MarginBase. The borrow rate increases with utilization so that lightly used pools stay efficient while highly utilized pools become progressively more expensive to borrow from.

Utilization Rate

At the contract level, utilization is computed from the pool's mirror reserve relative to the total borrow-side reserve:

$$u=\frac{\text{mirrorReserve}}{\text{realReserve}+\text{mirrorReserve}}$$

This is equivalent to measuring how much of the borrow-side reserve is already mirrored into active debt.

Interest Rate Calculation

The implementation in InterestMath.getBorrowRateByReserves() applies three cumulative segments:

1. Low Utilization Phase

When utilization is below $U_{\text{medium}}$, the rate increases linearly from the base rate:

$$r=r_{\text{base}}+u\times m_{\text{low}}$$

• rateBase (r_base): Base borrow rate.
• u: Utilization rate.
• mLow (m_low): Slope applied before the medium threshold.

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2. Medium Utilization Phase

Once utilization reaches $U_{\text{medium}}$, the medium slope is added on top of the low-utilization segment:

$$r=r_{\text{base}}+U_{\text{medium}}\times m_{\text{low}}+(u-U_{\text{medium}})\times m_{\text{medium}}$$

• useMiddleLevel (U_medium): Medium utilization threshold.
• mMiddle (m_medium): Slope applied between the medium and high thresholds.

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3. High Utilization Phase

Above $U_{\text{high}}$, the high-utilization slope is layered on top of both prior segments:

$$r=r_{\text{base}}+U_{\text{medium}}\times m_{\text{low}}+(U_{\text{high}}-U_{\text{medium}})\times m_{\text{medium}}+(u-U_{\text{high}})\times m_{\text{high}}$$

• useHighLevel (U_high): High utilization threshold.
• mHigh (m_high): Slope applied once utilization exceeds the high threshold.

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Default Parameters

The deployed defaults are initialized in MarginBase as raw marginState values, where 1,000,000 = 100%.

Parameter	Contract field	Description	Default Value
r_base	rateBase	Base interest rate	20000 (2%)
m_low	mLow	Slope for low utilization phase	10
U_medium	useMiddleLevel	Medium utilization threshold	300000 (30%)
m_medium	mMiddle	Slope for medium utilization phase	100
U_high	useHighLevel	High utilization threshold	700000 (70%)
m_high	mHigh	Slope for high utilization phase	10000