Interest Rates Model

Interest rates for Lender Investors (Deposit APR) and Leveraged LP Farmers (Borrow APR).

The interest rates model CygnusDAO uses is based on Compound's formula for lending and borrowing, using utilization rate as a determinant.

Utilization Rate refers to the percentage amount of the lending pool that being used:

$$U_x = \frac{Borrows_x}{(Cash_x+Borrows_x-Reserves_x)}$$

Borrows is the amount of $x$ borrowed.

Cash is the amount of $x$ left in the pool.

Reserves is the portion of borrower interest that is converted into reserves and controlled by the Cygnus DAO.

$$DepositAPR_x = BorrowAPR_x*U_x*(1-ReserveFactor_x)$$

$$BorrowAPR_x = BaseRate +Multiplier * min(U_x, KINK) +\\ JumpMultiplier*max(U_x-KINK,0)$$

ReserveFactor is the current reserve factor for the market, set at 5% by default

Base Rate is the Borrow interest rate when utilization is 0%.

Multiplier is the rate of increase in interest rate with respect to utilization and is derived from the Farm's APR.

KINK is the point in the utilization rate in which the model follows the jump multiplier, set at 90% by default.

Jump Multiplier is the rate of increase in interest rate with respect to utilization after the KINK and it is used to ensure the supply of the pool.

The slope of the interest rate is dictated by the Liquidity Token APR. If a pool such as weth-usdc has a much higher APR since it earns from more trading fees and rewards, then to borrow using weth-usdc as collateral has a higher interest rate than a pool with lower APR. The interest rate is set once the pool is deployed, and should only be upgraded by the DAO with sufficient time in advance to give the users of the pool sufficient notice.

At 80% Utilization Rate, our Jump Rate Multiplier starts to discourage borrowing to prevent a situation where Lender Investors can’t withdraw due to full-utilization.