Each redemption event contributes to an increment in the baseRate, which then gradually recedes over time, considering the span since the last fee occurrence. The formula for calculating the redemption fee involves the expression (baseRate + 0.5%) * borrowed USDA, with baseRate representing the adjusted fee rate and borrowed USDA indicating the loaned amount.
In each redemption, the base rate is augmented based on the proportion of redeemed USDA, aligned with the prevailing supply of USDA. This is mathematically outlined as follows:
where b(t) stands for the base rate at time t, m represents the redeemed USDA amount, n symbolizes the current supply of USDA, and α is a constant parameter set at 0.5.
The base rate experiences a gradual decay over time due to a decay factor that is applied with each instance of USDA redemption or issuance before computing the resulting fee. This decay process takes the following form:
where δ stands for the decay factor (e.g., 0.94), and △t corresponds to the time elapsed since the most recent redemption or loan issuance. The selection of the decay factor δ is such that it aligns with a half-life of 12 hours for the base rate.