Interest Rate Model

Based on Aave Protocol, https://docs.aave.com/risk/liquidity-risk/borrow-interest-rate.

Liquidity risk materializes when utilization 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 utilization rate $U_{optimal}$. Before $U_{optimal}$the slope is small, after it starts rising sharply.

The interest rate$R_t$follows the model:

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

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

Both the variable and stable interest models, are derived from the formula above from the Whitepaper with different parameters for each asset.

• When $U < U_{optimal}$ the borrow interest rates increase slowly with utilization

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

Variable loans see their rate constantly evolving with utilization. This means they are not ideal for financial planning.

Hence stable loans, that maintain their interest rate at issuance until the specific rebalancing conditions are met. For rebalancing the stable rate down, the loans stable rate$S$needs to be greater than the current stable rate$S_t$ plus a delta equal to 20%: $S \geq S_t + 20\%$.

For rebalancing the stable rate up, these two conditions need to be met:

1. Utilization Rate: $U_t > 95\%$

2. Overall Borrow Rate, the weighted average of all the borrow rates: $R_O < 25\%$

Variable Interest Rate Model Parameters

 Asset Uoptimal Base Slope 1 Slope 2 Binance 45% 0% 8% 100% BUSD 60% 1% 4% 100% Bitcoin 45% 0% 8% 100% USDC 70% 1% 7% 60% Tether 70% 1% 7% 60% DAI 60% 1% 7% 150% Ethereum 45% 0% 8% 100% LINK 45% 0% 7% 300% ADA 45% 0% 7% 300% DOT 45% 0% 7% 300% LTC 45% 0% 7% 300%

Stable Interest Rate Model Parameters

 Asset Uoptimal Base Slope 1 Slope 2 Binance 45% 3% 10% 100% BUSD 60% 3.5% 6% 100% Bitcoin 45% 3% 10% 100% USDC 70% 3.5% 6% 60% Tether 70% 3.5% 6% 60% DAI 60% 3.5% 6% 150% Ethereum 45% 3% 10% 100% LINK 45% 3% 10% 300% ADA 45% 3% 10% 300% DOT 45% 3% 10% 300% LTC 45% 3% 10% 300% BCH 45% 3% 10% 300%

Interest Rate Curves

This section shows Multi-Chain Lend (MCL) Protocol’s interest rate curves per asset.

USDC | USDT

BNB | BTC | ETH