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.

To retrieve the interest rate strategy contract on-chain, see this section of the developer docs.

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 calculateCompoundedInterest method relies on an approximation that mostly affects high interest rates. The resulting actual borrow rate can is:

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

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. Current supply rate $\leq$ maximum variable rate * 40%

Smart Contract Reference

Model Parameters

The interest rate parameters have been calibrated per cluster of currencies that share similar risk profiles. First, it's crucial to distinguish assets that are used predominantly as collateral (volatile assets) which need liquidity at all times to enable liquidations. These assets require a low Optimal Utilisation rate typically calibrated around 45%. Secondly, the asset's liquidity on Aave is an important factor as the more liquidity, the more stable the utilisation: interest rates of assets with lower liquidity should be more conservative. For example lower liquidity stablecoins have lower Optimal Utilisation Ratio than those with higher liquidity.

It's also key to consider market conditions: how can the asset be used in the current market? Aave'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 Aave to take advantage of higher yield opportunities.

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.

Following the favorable historical review of liquidity risk, the interest rate models have been optimised to be more competitive while keeping theirs risk mitigation properties.

Variable Interest Rate Model Parameters

Asset	$U_{optimal}$	Base	Slope 1	Slope 2
AMPL	75%	0%	2%	10,000%
BUSD	80%	0%	4%	100%
DAI	80%	0%	4%	75%
GUSD	80%	0%	4%	100%
PAX	90%	0%	4%	60%
RAI	80%	0%	4%	75%
sUSD	80%	0%	4%	100%
TUSD	80%	0%	4%	75%
USDC	90%	0%	4%	60%
USDT	90%	0%	4%	60%
AAVE
BAL	45%	0%	7%	300%
BAT	45%	0%	7%	300%
CRV	45%	0%	7%	300%
DPI
ENJ	45%	0%	7%	300%
ETH	65%	0%	8%	100%
KNC
LINK	45%	0%	7%	300%
MANA	45%	0%	7%	300%
MKR	45%	0%	7%	300%
REN	45%	0%	7%	300%
REP	45%	0%	7%	150%
SNX	80%	3%	12%	100%
UNI	45%	0%	7%	300%
WBTC	65%	0%	7%	100%
XSUSHI
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. Current supply rate $\leq$ maximum variable rate * 40%

Smart Contract Reference

The currencies the most exposed to liquidity risk do not offer stable rate borrowing.

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

Asset	$U_{optimal}$	Base	Slope 1	Slope 2
AMPL
BUSD
DAI	80%	4%	2%	75%
GUSD
PAX
RAI
sUSD
TUSD	80%	4%	2%	75%
USDC	90%	4%	2%	60%
USDT	90%	3.5%	2%	60%
AAVE
BAL
BAT	45%	3%	10%	300%
CRV
ENJ	45%	3%	10%	300%
ETH	65%	3%	10%	100%
KNC	65%	3%	10%	300%
LINK	45%	3%	10%	300%
MANA	45%	3%	10%	300%
MKR	45%	3%	10%	300%
REN
SNX
UNI
WBTC	65%	3%	10%	60%
XSUSHI
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

Interest Rate Parameters Updates from V1 to V2

Interest Rate Curves

This section shows Aave's APY per asset. ​

AMPL

Please note the AMPL interest rate model is extreme due to the rebasing nature of the token

BUSD | GUSD | sUSD

DAI | TUSD

USDC | USDT

BAL | BAT | CRV | ENJ | LINK | MANA | MKR | REN | WBTC | UNI | YFI | ZRX

No stable borrows for BAL, CRV, REN and YFI

SNX

WETH

Related Smart Contracts

	Token	aToken	Stable Debt Token	Variable Debt Token	Interest Rate Strategy
BUSD	0x4fabb145d64652a948d72533023f6e7a623c7c53	0xA361718326c15715591c299427c62086F69923D9		0xbA429f7011c9fa04cDd46a2Da24dc0FF0aC6099c	0x26D40544447F68a3De69005822195549934624B9
DAI	0x6b175474e89094c44da98b954eedeac495271d0f	0x028171bCA77440897B824Ca71D1c56caC55b68A3	0x778A13D3eeb110A4f7bb6529F99c000119a08E92	0x6C3c78838c761c6Ac7bE9F59fe808ea2A6E4379d	0xfffE32106A68aA3eD39CcCE673B646423EEaB62a
GUSD	0x056fd409e1d7a124bd7017459dfea2f387b6d5cd	0xD37EE7e4f452C6638c96536e68090De8cBcdb583		0x279AF5b99540c1A3A7E3CDd326e19659401eF99e	0x2893405d64a7Bc8Db02Fa617351a5399d59eCf8D
sUSD	0x57ab1ec28d129707052df4df418d58a2d46d5f51	0x6C5024Cd4F8A59110119C56f8933403A539555EB		0xdC6a3Ab17299D9C2A412B0e0a4C1f55446AE0817	0x3082D0a473385Ed2cbd1f16087ab8b7BF79f0355
TUSD	0x0000000000085d4780b73119b644ae5ecd22b376	0x101cc05f4A51C0319f570d5E146a8C625198e636	0x7f38d60D94652072b2C44a18c0e14A481EC3C0dd	0x01C0eb1f8c6F1C1bF74ae028697ce7AA2a8b0E92	0x0DdEC679166C367ae45036c8b2c169C5FB2dceE1
USDC	0xa0b86991c6218b36c1d19d4a2e9eb0ce3606eb48	0xBcca60bB61934080951369a648Fb03DF4F96263C	0xE4922afAB0BbaDd8ab2a88E0C79d884Ad337fcA6	0x619beb58998eD2278e08620f97007e1116D5D25b	0x8Cae0596bC1eD42dc3F04c4506cfe442b3E74e27
USDT	0xdac17f958d2ee523a2206206994597c13d831ec7	0x3Ed3B47Dd13EC9a98b44e6204A523E766B225811	0xe91D55AB2240594855aBd11b3faAE801Fd4c4687	0x531842cEbbdD378f8ee36D171d6cC9C4fcf475Ec	0x515E87cb3fec986050F202a2bbfa362A2188bc3F
AAVE	0x7fc66500c84a76ad7e9c93437bfc5ac33e2ddae9	0xFFC97d72E13E01096502Cb8Eb52dEe56f74DAD7B
BAT	0x0d8775f648430679a709e98d2b0cb6250d2887ef	0x05Ec93c0365baAeAbF7AefFb0972ea7ECdD39CF1	0x277f8676FAcf4dAA5a6EA38ba511B7F65AA02f9F	0xfc218A6Dfe6901CB34B1a5281FC6f1b8e7E56877	0xBdfC85b140edF1FeaFd6eD664027AA4C23b4A29F
CRV	0xd533a949740bb3306d119cc777fa900ba034cd52	0x8dAE6Cb04688C62d939ed9B68d32Bc62e49970b1		0x00ad8eBF64F141f1C81e9f8f792d3d1631c6c684	0xE3a3DE71B827cB73663A24cDB6243bA7F986cC3b
ENJ	0xf629cbd94d3791c9250152bd8dfbdf380e2a3b9c	0xaC6Df26a590F08dcC95D5a4705ae8abbc88509Ef	0x943DcCA156b5312Aa24c1a08769D67FEce4ac14C	0x38995F292a6E31b78203254fE1cdd5Ca1010A446	0x4a4fb6B26e7F516594b7242240039EA8FAAc897a
KNC	0xdd974d5c2e2928dea5f71b9825b8b646686bd200	0x39C6b3e42d6A679d7D776778Fe880BC9487C2EDA	0x9915dfb872778B2890a117DA1F35F335eb06B54f	0x6B05D1c608015Ccb8e205A690cB86773A96F39f1	0xFDBDa42D2aC1bfbbc10555eb255De8387b8977C4
LINK	0x514910771af9ca656af840dff83e8264ecf986ca	0xa06bC25B5805d5F8d82847D191Cb4Af5A3e873E0	0xFB4AEc4Cc858F2539EBd3D37f2a43eAe5b15b98a	0x0b8f12b1788BFdE65Aa1ca52E3e9F3Ba401be16D	0xED6547b83276B076B771B88FcCbD68BDeDb3927f
MANA	0x0f5d2fb29fb7d3cfee444a200298f468908cc942	0xa685a61171bb30d4072B338c80Cb7b2c865c873E	0xD86C74eA2224f4B8591560652b50035E4e5c0a3b	0x0A68976301e46Ca6Ce7410DB28883E309EA0D352	0x004fC239848D8A8d3304729b78ba81d73d83C99F
MKR	0x9f8f72aa9304c8b593d555f12ef6589cc3a579a2	0xc713e5E149D5D0715DcD1c156a020976e7E56B88	0xC01C8E4b12a89456a9fD4e4e75B72546Bf53f0B5	0xba728eAd5e496BE00DCF66F650b6d7758eCB50f8	0xE3a3DE71B827cB73663A24cDB6243bA7F986cC3b
REN	0x408e41876cccdc0f92210600ef50372656052a38	0xCC12AbE4ff81c9378D670De1b57F8e0Dd228D77a	0x3356Ec1eFA75d9D150Da1EC7d944D9EDf73703B7	0xcd9D82d33bd737De215cDac57FE2F7f04DF77FE0	0x9B1e3C7483F0f21abFEaE3AeBC9b47b5f23f5bB0
SNX	0xc011a72400e58ecd99ee497cf89e3775d4bd732f	0x35f6B052C598d933D69A4EEC4D04c73A191fE6c2		0x267EB8Cf715455517F9BD5834AeAE3CeA1EBdbD8
UNI	0x1f9840a85d5af5bf1d1762f925bdaddc4201f984	0xB9D7CB55f463405CDfBe4E90a6D2Df01C2B92BF1		0x5BdB050A92CADcCfCDcCCBFC17204a1C9cC0Ab73	0x24ABFac8dd8f270D752837fDFe3B3C735361f4eE
WBTC	0x2260fac5e5542a773aa44fbcfedf7c193bc2c599	0x9ff58f4fFB29fA2266Ab25e75e2A8b3503311656	0x51B039b9AFE64B78758f8Ef091211b5387eA717c	0x9c39809Dec7F95F5e0713634a4D0701329B3b4d2	0xf41E8F817e6C399d1AdE102059c454093b24f35B
WETH	0xc02aaa39b223fe8d0a0e5c4f27ead9083c756cc2	0x030bA81f1c18d280636F32af80b9AAd02Cf0854e	0x4e977830ba4bd783C0BB7F15d3e243f73FF57121	0xF63B34710400CAd3e044cFfDcAb00a0f32E33eCf	0x4ce076b9dD956196b814e54E1714338F18fde3F4
YFI	0x0bc529c00c6401aef6d220be8c6ea1667f6ad93e	0x5165d24277cD063F5ac44Efd447B27025e888f37		0x7EbD09022Be45AD993BAA1CEc61166Fcc8644d97	0xfd71623D7F41360aefE200de4f17E20A29e1d58C
ZRX	0xe41d2489571d322189246dafa5ebde1f4699f498	0xDf7FF54aAcAcbFf42dfe29DD6144A69b629f8C9e	0x071B4323a24E73A5afeEbe34118Cd21B8FAAF7C3	0x85791D117A392097590bDeD3bD5abB8d5A20491A	0x1a4babC0e20d892167792AC79618273711afD3e7)

Deposit APY

The borrow interest rates paid are distributed as yield for aToken holders who have deposited in the protocol, excluding a share of yields sent to the ecosystem reserve defined by the reserve factor. 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:

$D_t = U_t ( SB_t S_t + VB_t V_t)(1-R_t)$

• $U_t$, 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

• $R_t$, the reserve factor

You can view the protocol's deposit APY on the Aave App for each asset.

The average Deposit APY over a period also includes Flash Loan fees.