Deposit Rate Subsidization

Lucra Protocol's deposit rate stability is supported by borrow demand from borrower NEP distribution and direct subsidization. Lucra defines a target deposit rate ($r_{target}$), and a threshold deposit rate ($r_{threshold}$) and constantly attempts to retain a deposit rate close to $r_{target}$ and always above $r_{threshold}$.

Every epoch, the average deposit rate during the last epoch ($r_{current}$) is calculated and compared with the target and threshold rates. Appropriate measures are then made to readjust the deposit rate.

Borrower NEP Incentives

Lucra's deposit rate is primarily adjusted by calibrating the rate of NEP emission to borrowers ($e$), updated through a feedback control algorithm.

NEP Emission Feedback Control

Lucra alters the NEP emission rate based on a multiplicative increase / multiplicative decrease feedback control algorithm, which adjusts the NEP emission rate of the next epoch $e_{n+1}$ based on the previous emission rate of $e_n$:

$$e_{n+1} = k \cdot e_n$$

The feedback control algorithm adjusts incentives with $r_{average}$ - the average of $r_{target}$ and $r_{threshold}$ - as the reference point:

$$r_{average}=\frac{r_{target}+r_{threshold}}{2}$$

• If deposit rate is approaching the threshold ($r_{current} < \frac{r_{threshold}+r_{average}}{2}$), increase emission by 0.7% ($k \approx 1.007$)
• If deposit rate approaches the target ($r_{current} > \frac{r_{target}+r_{average}}{2}$), reduce emission by 0.3% ($k \approx 0.997$)

where the set $k$ values result in a 50% emission increase over a week-long period or a 15% decrease over a week-long period.

Direct Subsidization

As an additional layer of safety, the protocol directly subsidizes the deposit rate if it is below the threshold rate ($r_{current}<r_{threshold}$), funded from the yield reserve's stockpiled stablecoins.

An amount required to raise the deposit rate to the threshold is distributed to depositors, which is limited to 15% of the yield reserve's balance per subsidization to prevent excessive drainage. Distributed subsidies are added to the money market’s liquidity, increasing the lNEP exchange rate and appreciating the value of lNEP.