Mitigating liquidity risk through the borrow interest rate model

Aaveâ€™s interest rate strategy is calibrated to manage liquidity risk and optimise utilization. The borrow interest rates come from the Utilization Rate $U$.

â€‹$U$is an indicator of the availability of capital in the pool. The interest rate model is used to manage liquidity risk through user incentivizes 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.

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:

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

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

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:

Utilization Rate: $U_t > 95\%$

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

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 utilization on Aaveâ€™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 utilized 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.

Asset | $U_{optimal}$â€‹ | Base | Slope 1 | Slope 2 |

BUSD | 80% | 1% | 4% | 50% |

DAI | 90% | 1% | 7% | 60% |

sUSD | 80% | 1% | 4% | 50% |

TUSD | 80% | 1% | 4% | 50% |

USDC | 90% | 1% | 7% | 60% |

USDT | 90% | 1% | 7% | 60% |

BAT | 45% | 0% | 7% | 300% |

ENJ | 45% | 0% | 7% | 300% |

ETH | 80% | 0% | 8% | 50% |

KNC | 80% | 0% | 8% | 50% |

LEND | 80% | 0% | 7% | 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% | 50% |

WBTC | 80% | 0% | 8% | 50% |

ZRX | 45% | 0% | 7% | 300% |

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:

Utilization Rate: $U_t > 95\%$

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 | $U_{optimal}$â€‹ | Base | Slope 1 | Slope 2 |

BUSD | â€‹ | â€‹ | â€‹ | â€‹ |

DAI | 90% | 3.5% | 6% | 60% |

sUSD | â€‹ | â€‹ | â€‹ | â€‹ |

TUSD | â€‹ | â€‹ | â€‹ | â€‹ |

USDC | 90% | 3.5% | 6% | 60% |

USDT | 90% | 3.5% | 6% | 60% |

BAT | 45% | 3% | 10% | 300% |

ENJ | â€‹ | â€‹ | â€‹ | â€‹ |

ETH | 80% | 3% | 10% | 60% |

KNC | 80% | 3% | 10% | 60% |

LEND | 80% | 3% | 10% | 300% |

LINK | 45% | 3% | 10% | 300% |

MANA | 80% | 3% | 10% | 60% |

MKR | 45% | 3% | 10% | 300% |

REN | â€‹ | â€‹ | â€‹ | â€‹ |

REP | 45% | 3% | 10% | 150% |

SNX | â€‹ | â€‹ | â€‹ | â€‹ |

WBTC | 80% | 3% | 10% | 60% |

ZRX | 45% | 3% | 10% | 300% |

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.

No stable borrows for ENJ and REN

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:

â€‹$D_t = U_t ( SB_t S_t + VB_t V_t)$

â€‹$U_t$, the utilization ratio

â€‹$SB_t$, the stable borrows

â€‹$S_t$, the average stable rate

â€‹$VB_t$, the variable borrows

â€‹$V_t$, the variable rate

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