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Interest Rate Model
The protocol has interest rates that are designated per market from both the supply side and the borrowing side. For each market, total Borrowing B and deposit S, the utilization ratio U is defined as follows:
U=B/S
The Interest Rate Index 𝐼 is calculated each time a transaction occurs:
πΌπ‘˜,π‘š =πΌπ‘˜βˆ’1,π‘š* (1+π‘Ÿ*𝑑)
Therefore, total borrowing in a market is given by:
Borrowingπ‘˜,π‘š =Borrowingπ‘˜βˆ’1,π‘š*(1+π‘Ÿ*𝑑)
A portion of the interest is kept as reserve, set by reserve factor πœ†:
reservesm =reservesπ‘˜βˆ’1,π‘š + Debtπ‘˜βˆ’1,π‘š*(π‘Ÿ*𝑑*πœ†)
The interest rates provided for markets that can be borrowed or supplied are dynamic and have a yield curve that varies based on utilizations.
𝛼L+ 𝛽Lβˆ—π‘ˆ)(1 + 𝑆), 𝑖𝑓 π‘ˆβ‰€π‘ˆL
ib = 𝛼+ π›½βˆ—π‘ˆ
𝛼+ π›½βˆ—π‘ˆT + 𝛾(π‘ˆβˆ’π‘ˆT), 𝑖𝑓 π‘ˆβ‰₯π‘ˆT
Below UL: lower the interest rate to foster borrowing demand
Above UT: increase the interest rate sharply to boost liquidity providing incentives
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