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.

USDC | USDT

DAI

TUSD | sUSD | BUSD

SNX

MANA | ETH | WBTC

KNC

LEND

BAT | ENJ | LINK | MKR | REN | REP | YFI | ZRX

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.