Model for Perpetual loans

Interest Rate Model

Liquidity risk materializes when utilization is high, it becomes more problematic as gets closer to 100%. To tailor the model to this constraint, the interest rate curve is split into two parts around an optimal utilization rate $U_{optimal}$. Before $U_{optimal}$ the slope is small, after it starts rising sharply.

The interest rate $R_t$ for Perpetual loans follows the model:

$if U < U_{optimal}: R_t = (R_o + U_t / U_{optimal} * R_{slope1})*(1+0.15)$

$if U \ge U_{optimal}: R_t = (R_o + R_{slope1} + (U_t - U_{optimal}) / (1 - U_{optimal}) * R_{slope2}) *(1+0.15)$

With *(1+0.15) being the additional 15% fees on borrow rate

Model Parameters

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

When market conditions change, the interest rate parameters can be adapted. These changes must adapt to utilization on FRAKT’s market.

Asset	Uoptimal	Ro	Rslope1	Rslope2
SOL	50%	3%	40%	100%

Borrow Interest Rate Curve

Deposit APY

The borrow interest rates paid are distributed as yield for lenders who have deposited in the protocol, excluding a share of yields sent to the ecosystem reserve and another share going to FRAKT as revenue. 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:

$D_t = (U_t * B_t * (1-R_t))$

$U_t$: the utilisation ratio.

$B_t$: the variable borrow rate.

$R_t$: the reserve factor.

Deposit Interest Rate Curve

Deposit Interest Rate Model

You can view the protocol's deposit APY on the FRAKT App