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:

𝐼𝑘,𝑚 =𝐼𝑘−1,𝑚* (1+𝑟*𝑡)

Therefore, total borrowing in a market is given by:

Borrowing𝑘,𝑚 =Borrowing𝑘−1,𝑚*(1+𝑟*𝑡)

A portion of the interest is kept as reserve, set by reserve factor 𝜆:

reservesm =reserves𝑘−1,𝑚 + Debt𝑘−1,𝑚*(𝑟*𝑡*𝜆)

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+ 𝛽L∗𝑈)(1 + 𝑆), 𝑖𝑓 𝑈≤𝑈L

ib = 𝛼+ 𝛽∗𝑈

𝛼+ 𝛽∗𝑈T + 𝛾(𝑈−𝑈T), 𝑖𝑓 𝑈≥𝑈T

Below UL: lower the interest rate to foster borrowing demand

Above UT: increase the interest rate sharply to boost liquidity providing incentives