explain formula for aave v3 utilization curve

Aave V3 Utilization Curve and Formula

The Aave V3 utilization curve is a mechanism used to dynamically determine the interest rates for borrowing and lending assets based on the demand for liquidity in a reserve 1.

Utilization Rate Formula

The fundamental formula for calculating the Utilization Rate ((U)) in a lending protocol like Aave is the ratio of the total borrowed assets to the total available liquidity 23.
The formula is expressed as:
$$ U = \frac{\text{TotalBorrows}}{\text{TotalLiquidity}} $$ 2
Where:
  • ( U ): Represents the utilization rate or ratio 2.
  • TotalBorrows: The total amount of a specific asset that has been borrowed from the pool 2.
  • TotalLiquidity: The total available supply of that asset in the system 2.
A higher utilization rate indicates greater borrowing activity relative to the available liquidity 23.

The Utilization Curve Mechanism

The utilization curve dictates how the Annual Percentage Rate (APR) for borrowing and lending changes as the utilization rate ((U)) fluctuates 1. This dynamic interest rate model is designed to maintain a healthy balance between supply and demand for liquidity 1.
Key characteristics of the curve include:
  • Optimal Utilization ((U_{optimal})): The curve features a specific point, often around 75%, known as the optimal utilization rate 1.
  • Pre-(U_{optimal}) Rates: When the utilization rate is below (U_{optimal}), the APR remains relatively flat and low, which incentivizes borrowing 1.
  • Post-(U_{optimal}) Rates: Once the utilization rate surpasses (U_{optimal}), the APR increases sharply 1. This aggressive rate hike serves two purposes:
    1. To deter further overutilization of the pool 1.
    2. To incentivize depositors to supply more liquidity to the reserve 1.
This mechanism ensures that sufficient liquidity remains available for withdrawals while appropriately rewarding lenders and charging borrowers 1.
Since its launch, Aave V3 has seen significant adoption, with its utilization rates often surpassing those of Aave V2 4.
For example, by June 2022, Aave V3 utilization had reached a peak of 67%, significantly higher than the 45% all-time high of Aave V2 4. Furthermore, stablecoin utilization on Ethereum, which reflects activity on Aave V3 since its launch in March 2022, saw a marked increase, peaking at approximately 58% by the end of 2022 5.
Utilization rates for specific assets, such as wrapped Ether (wETH) lending on Aave V3, trended upward throughout 2023, ranging from 42% in January to 68% in June 6.
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