📈Interest Rate Models

Interest rate curves

Interest rate models in traditional lending pools

This mechanism is similar to the interest rate curve used in traditional lending pools.

The curve is characterized by two parameters:

• $r_{90\%}$, which is the rate at $u_{target}=90\%$

• $c=4$, a fixed parameter that determines the steepness of the curve above and below the utilization target.

The aim of the Curve Mechanism is to manage short-term utilization.

Interest rate model used in Natrium

This mechanism continuously shifts the curve to adjust to market conditions over time.

Note that the rate follows the shift of the curve. This means that the rate is continuously evolving over time, even when there is no interaction.

The shifting of the curve is done by continuously changing the value of $r_{90\%}$ over time:

• When the utilization is above the target utilization, $r_{90\%}$ continuously shifts upwards.

• When the utilization is below the target utilization, $r_{90\%}$ continuously shifts downwards.

The speed at which $r_{90%}$ moves is updated at each interaction: the farther we are from the target, the faster $r_{90%}$, hence the curve, shift.