Interest Rate Model

Helios derives interest rates to one on-chain variable—utilization. A gentle slope applies while utilization is below an optimal point; a much steeper slope applies above it, protecting exit liquidity in stress. Depositors earn

Supply APR = Borrow APR × Utilization × (1 – Reserve-Factor)

where the reserve-factor funds the protocol treasury.

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1 Why Utilization Drives Rates

Utilization (U) = Borrowed BTC / Total BTC in the reserve

• Low U → slack liquidity → cheap leverage.

• High U → scarce liquidity → rising APR to deter new borrows and attract deposits.

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2 Borrow-Rate Curve

Parameter	Symbol	Typical setting*	Purpose
Base rate	r₀	0 – 1 %	Floor APR when U ≈ 0
Optimal utilization	U*	70 – 85 %	“Kink” where slope changes
Slope 1	m₁	2 – 8 %	Mild gradient below the kink
Slope 2	m₂	30 – 200 %	Steep gradient above the kink
Reserve-factor	f	5 – 20 %	Protocol share of interest

Piece-wise formula

              { r₀ + m₁ · (U / U*)                      if U ≤ U*
Borrow APR =
              { r₀ + m₁ + m₂ · (U – U*) / (1 – U*)      if U > U*

• Below the kink the curve is shallow, encouraging leverage.

• Above the kink the curve is steep, preserving liquidity.

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3 Supply (Liquidity) Rate

LiquidityRate (rₗ) = Borrow APR × U × (1 – f)

Balances in hTokens rebase automatically whenever the pool’s liquidity index updates; users never pay gas to claim yield.

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4 Governance Levers

Lever	When to adjust	What it does
r₀	Macro too tight / loose	Shifts the whole curve up / down
U*	Volatility changes	Moves the kink left / right
m₁	Encourage / dampen moderate borrowing	Tilts slope below kink
m₂	Strengthen liquidity defense	Tilts slope above kink
f	Treasury runway vs. depositor yield	Widens / narrows the supply–borrow spread

All levers live in a single Interest-Rate Strategy contract that governance can swap out without touching user balances.

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5 Key Takeaways

• Utilization drives everything—keep an eye on the pool dashboard.

• Supply APR = Borrow APR × U × (1 – f).