Variable Interest Rate Parameters

Introduction

The interest rate parameters have been calibrated per cluster of currencies that share similar risk profiles.

Molend’s adopts an interest rate model that scales with utilization rate, for both depositing and borrowing interest rates. When utilization rate is high, the interest incurred on borrowers will scale up, similar to that of interest payout to depositors, encouraging more deposited assets to maintain protocol solvency.

Utilization Rate

Molend’s interest rate strategy is calibrated to manage liquidity risk and optimise utilisation.

$U$is an indicator of the availability of capital in the pool. The interest rate model is used to manage liquidity risk through user incentivises to support liquidity:

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

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

Interest Rate Model

Liquidity risk materialises when utilisation is high, its 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 utilisation rate $U_{optimal}$. Before $U_{optimal}$the slope is small, after it starts rising sharply.

The interest rate$R_t$follows the model:

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

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

In the borrow rate technical implementation, the method relies on an approximation that mostly affects high interest rates. The resulting actual borrow rate can is:

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

• When $U < U_{optimal}$ the borrow interest rates increase slowly with utilisation
• When $U \geq U_{optimal}$ the borrow interest rates increase sharply with utilisation to above 50% APY if the liquidity is fully utilised.

Variable loans see their rate constantly evolving with utilisation.

Variable Interest Rate Model Parameters

For variable interest rates, it's crucial to distinguish assets that are used predominantly as collateral (volatile assets) which need liquidity at all times to enable liquidations.The asset's liquidity on Molend is an important factor as the more liquidity, the more stable the utilization: interest rates of assets with lower liquidity should be more conservative. For example lower liquidity stablecoins have lower Optimal Utilization Ratio than those with higher liquidity.

Market conditions are always crucial factors when considering the variable interest rates. How can the asset be used in the current market? Molend’s borrowing costs must be aligned with market yield opportunities. Or there would be a rate arbitrage with rational users incentivized to borrow all the liquidity on Molend to take advantage of higher yield opportunities.

Asset	$U_{optimal}$	Base	Slope 1	Slope 2
ETH	20%	0%	10%	100%
USDC	25%	0%	15%	100%
USDT	25%	0%	15%	100%