Productive Debt Math

Worked mathematical examples showing how LotusUSD productive debt compresses borrow-lend spreads, guarantees floor yields, and reduces rate volatility.

This page derives the formulas behind LotusUSD productive debt and walks through worked examples showing how it compresses borrow-lend spreads and guarantees floor yields.

Productive debt means lenders always earn the base rate. Utilization only determines how much additional yield they capture from the credit spread.

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Guaranteeing a floor yield

In traditional onchain lending markets, the supply rate for lenders is simply:

$$supplyRate = borrowRate * utilizationRate$$

Plaintext (for copy/paste):

supplyRate = borrowRate * utilizationRate

If the borrow rate is 5% and utilization is 50%, the supply rate is 2.5%. Lotus changes this calculation because the loan asset intrinsically earns the base rate. If the base rate is 3%, lenders earn at least 3% regardless of utilization.

Compressing the borrow-lend spread

With productive debt, the supply rate is calculated differently:

$$supplyRate = baseRate + (creditSpread * utilizationRate)$$

Plaintext (for copy/paste):

supplyRate = baseRate + (creditSpread * utilizationRate)

The borrow rate equals the base rate plus the credit spread:

$$borrowRate = baseRate + creditSpread$$

Plaintext (for copy/paste):

borrowRate = baseRate + creditSpread

With a 5% borrow rate and 3% base rate, the credit spread is 2%. At 50% utilization: supplyRate = 3% + (2% × 50%) = 4%, compared to 2.5% without productive debt.

This example allocates all productive-debt benefit to lenders. In practice the benefit splits between borrowers and lenders.

The result is higher supply rates and lower borrow rates.

Reducing rate volatility

Productive debt splits the borrow rate into a base rate and credit spread, reducing rate volatility. Most markets use an IRM where utilization drives the credit spread. Without productive debt, a utilization shock moves the entire borrow rate. With productive debt, the same shock only moves the credit spread, which is a fraction of the total rate.

LotusUSD serves as the loan asset in USD-denominated markets, though it is largely abstracted from the borrower and lender experience. Users can mint and redeem LotusUSD directly for low-risk yield.