CLP Supply Rate

Twyne integrates three distinct interest rates:

• Lending market yield
• Lending market borrow
• Credit LP supply rates

The first two guarantee that all assets delegated onto Twyne continue to earn/pay whatever yield is paid/charged by the underlying lending market.

CLP Supply Rate

The CLP supply rate is the rate at which a borrower’s collateral is charged for reserving the borrowing power offered by CLPs. Twyne employs a curved interest rate model IR(u) that depends solely on the asset-specific utilization rate of CLPs:
u ≡ CLP / C_total_LP

With asset-specific parameters IR₀, u₀, IR_max, and γ:
IR(u) = (IR₀ / u₀) · u + (IR_max − (IR₀ / u₀)) · u^γ

Subject to consistency conditions:

• IR_max > IR₀ / u₀ > 0
• γ > 1
• 1 > u₀ > 0

[FIGURE PLACEHOLDER]
Figure 1 shows example curves plotted for various values of γ.
Sample curves: IR₀ = 0.1, u₀ = 0.8, IR_max = 1.2, varying γ.
Utilization and interest rates have been converted from decimals to percents.

Model Behavior

This equation is designed to behave quasi-linearly for utilization rates u_asset ≤ u₀ and ramp quickly to IR_max (with power γ) once u₀ is exceeded. The curve, initially used by Keom Protocol, creates efficient one-dimensional interest rate shapes without needing complex on-chain operations or PID controllers.

Parameters are intuitively similar to the linear-kink model (black dot-dashed curve in Figure 1):

• u₀ and IR₀ define the kink location and rate.
• γ controls how sharply the curve overshoots at the kink and how much it lags behind the linear model at high utilization.

Borrower Siphoning Rate

In return for increased credit capacity, borrowers pay interest from their collateral directly to Credit LPs — called the Borrower Siphoning Rate (r_C).

Borrower’s Perspective

For the borrower, collateral yield = subtractive rate r_C (paid to CLPs) plus any positive lending yield from the underlying market. Their borrow interest rate aligns with the underlying lending market’s quoted borrow rate.

Gross Interest Rate (r_C)

The gross interest rate paid to CLPs (in units of the borrower’s collateral asset) is:
r_C = (CLP · IR(u)) / C

Where:

• CLP = reserved funds
• IR(u) = utilization-based interest rate
• C = borrower’s collateral

Net Interest Rate (r_net_C)

The net rate r_net_C paid by the borrower is:
r_net_C = (CLP · IR(u)) / (C − B) = r_C / (1 − λ_twyne)

Where:

• B = borrower’s outstanding borrow
• λ_twyne = borrower’s Loan-to-Value on Twyne