Interest Rate Model

# Interest Rate Model

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:
β
$if \hspace{1mm} U < U_{optimal}: \hspace{1cm} R_t = R_0 + \frac{U_t}{U_{optimal}} R_{slope1}$
β
$if \hspace{1mm} U \geq U_{optimal}: \hspace{1cm} R_t = R_0 + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}}R_{slope2}$
β
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. 1.
Utilization Rate:
$U_t > 95\%$
2. 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%
45%
0%
7%
300%
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%
45%
3%
10%
300%
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) Protocolβs interest rate curves per asset.
USDC | USDT
BNB | BTC | ETH