# Borrow Interest Rate

Mitigating liquidity risk through the borrow interest rate model

Aave’s interest rate strategy is calibrated to manage liquidity risk and optimise utilisation. The borrow interest rates come from the Utilisation Rate $U$.

$U$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:

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

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

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 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. 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. Utilisation Rate: $U_t > 95\%$

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

## Model Parameters

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

When market conditions change, the interest rate parameters can be adapted. These changes must adapt to utilisation on Aave’s market as well as to incentives across DeFi.

The interest rate curve of SNX is much higher than that of other assets due to the staking incentives of the Synthetix platform. This makes SNX the most utilised pool generating the highest yields.

With the rise of liquidity mining, Aave also adapted its cost of borrowing by lowering $U_{optimal}$ of the assets affected. This increased the borrow costs that are now partially offset by the liquidity reward.

### Variable Interest Rate Model Parameters

 Asset $U_{optimal}$ Base Slope 1 Slope 2 BUSD 80% 1% 4% 100% DAI 80% 1% 7% 150% sUSD 80% 1% 4% 100% TUSD 80% 1% 4% 150% USDC 90% 1% 7% 60% USDT 90% 1% 7% 60% BAT 45% 0% 7% 300% ENJ 45% 0% 7% 300% ETH 65% 0% 8% 100% KNC 65% 0% 8% 300% LINK 45% 0% 7% 300% MANA 80% 0% 8% 50% MKR 45% 0% 7% 300% REN 45% 0% 7% 300% REP 45% 0% 7% 150% SNX 80% 3% 12% 100% WBTC 65% 0% 8% 100% YFI 45% 0% 7% 300% ZRX 45% 0% 7% 300%

### Stable Interest Rate Model Parameters

The stable rate provides predictability for the borrower which comes at a cost, as the interest rates are higher than the variable rate. However the rate of a stable loan is fixed until the rebalancing conditions are met:

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

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

The currencies the most exposed to liquidity risk, TUSD, sUSD and BUSD, do not offer stable rate borrowing.

The base rate of the stable rate model correspond to the average market rate of the asset.

 Asset $U_{optimal}$ Base Slope 1 Slope 2 BUSD DAI 80% 3.5% 6% 150% sUSD TUSD USDC 90% 3.5% 6% 60% USDT 90% 3.5% 6% 60% BAT 45% 3% 10% 300% ENJ ETH 65% 3% 10% 100% KNC 65% 3% 10% 300% LEND 80% 3% 10% 300% LINK 45% 3% 10% 300% MANA 80% 3% 10% 60% MKR 45% 3% 10% 300% REN REP 45% 3% 10% 150% SNX WBTC 80% 3% 10% 60% YFI ZRX 45% 3% 10% 300%

## Interest Rate Parameters Change

When market conditions change, risks change. The utilisation of reserves is continuously monitored to check liquidity is available. In case of prolonged full utilisation, the interest rate parameters are adapted to mitigate any risks emerging from market conditions

 Date Asset Uoptimal Variable Rate Stable Rate 21/10/2020 WBTC 65% Slope 2 = 100% Slope 2 = 100% 21/10/2020 ETH 65% Slope 2 = 100% Slope 2 = 100% 21/10/2020 TUSD Slope 2 = 150% 21/10/2020 sUSD Slope 2 = 100% 21/10/2020 BUSD Slope 2 = 100% 16/09/2020 SNX Slope 2 =100% 14/09/2020 DAI 80% Slope 2 = 150% Slope 2 = 150% 14/09/2020 KNC 65% Slope 2 = 300% Slope 2 = 300%

## Interest Rate Curves

This section shows Aave's interest rate curves per asset. Please use this spreadsheet for an interactive view based on the current state of the protocol, or to simulate borrows.

### LEND

No stable borrows for ENJ, REN and YFI

## Deposit APY

The borrow interest rates paid are distributed as yield for aToken holders who have deposited in the protocol. This interest rate is paid on the capital that is lent out then shared among all the liquidity providers. The deposit APY, $D_t$, is:

$D_t = U_t ( SB_t S_t + VB_t V_t)$

• $U_t$, the utilisation ratio

• $SB_t$, the share of stable borrows

• $S_t$, the average stable rate

• $VB_t$, the share of variable borrows

• $V_t$, the variable rate

You can view the protocol's deposit APY on the Aave App for each asset or on this Aave spreadsheet to see the calculations.

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