Interest Rate Model

Overview

Lumen Money offers variable interest rates for markets using two different models: the Jump Rate Model and the Whitepaper Rate Model. Each market operates under one of these models with specifically set risk parameters at the market's inception. Moreover, some markets feature a stable rate.

Jump Rate Model

The Jump Rate Model uses the following formulas to calculate the interest:

For Borrow rate:

borrow_rate(u)=b+a1⋅kink+a1⋅min⁡(0,u−kink)+a2⋅max⁡(0,u−kink)

And, for Supply rate:

supply_rate(u)=borrow_rate(u)⋅us⋅(1−reserve_factor)

Where,

us=borrows/ (cash+borrows−reserves+badDebt)

The borrow rate employs different formulas when the utilization rate falls into two distinct ranges:

If u < kink:

borrow_rate(u)=a1⋅u+b

If u > kink:

borrow_rate(u)=a 1 ​ ⋅kink+a 2 ​ ⋅(u−kink)+b

Model Parameters

• a1: Variable interest rate slope1.

• a2: Variable interest rate slope2.

• b: Base rate per block (baseRatePerYear / blocksPerYear).

• kink: Optimal utilization rate, at which the variable interest rate slope shifts from slope1 to slope2.

• reserve_factor: Part of interest income withdrawn from the protocol, i.e., not distributed to suppliers.

The utilization rate (u) is defined as:

utilization_rate=(borrows+bad_debt)/(cash+borrows+bad_debt−reserves)

​Where:

• borrows: Amount of borrows in the market, in terms of the underlying asset, excluding bad debt.

• cash: Total amount of the underlying asset owned by the market at a specific time.

• reserves: Amount of the underlying asset owned by the market but unavailable for borrowers or suppliers, reserved for various uses defined by the protocol's tokenomics.

• bad_debt: After liquidators repay as much debt as possible, reducing collateral to a minimal amount, the remaining debt is tagged as bad debt. Bad debt doesn’t accrue interest.