How is the Health Factor (HF) calculated in DeFi lending protocols?

The Health Factor is the ratio of total discounted collateral to total borrowed debt: HF = sum(Collateral_i * LiquidationThreshold_i) / TotalBorrowed. When HF > 1.0, the position is solvent. If HF falls below 1.0, anyone can act as a liquidator to repay a portion of the debt in exchange for seizing collateral at a discount.

What is the two-slope kinked interest rate model?

DeFi protocols (like Aave and Compound) utilize a two-slope piece-wise function for interest rates. Below optimal utilization (U_optimal, typically 80% to 90%), the borrow APR rises gently with Slope 1. Once utilization crosses the kink, Slope 2 sharply escalates borrowing rates up to 60%+ to incentivize borrowers to repay loans and depositors to inject capital, preventing liquidity freezes.

Model #38 • Desk 7: Digital Assets & Crypto Derivatives

DeFi Lending Money Market & Liquidation Cascade Simulator

An institutional collateralized credit underwriter for decentralized money markets (Aave v3, Morpho Blue, Compound). Simulate collateral Health Factors ($HF$), two-slope kinked utilization interest rate jumps, liquidator bonus arbitrage, close factors, and protocol bad debt insolvency cascades during price shocks.

Stress Scenarios:

Borrower Position Parameters POSITION SIZING

Collateral Spot Benchmark ($) $2,450.00

Baseline price of primary collateral (WETH / wstETH).

Collateral Deposited (Units) 100.00 ETH

Gross pledged collateral quantity in the smart contract.

Principal Debt Borrowed ($) $160,000

Current principal loan liability (USDC / USDT stablecoins).

Liquidation Threshold (LT %) 85.0%

Max loan-to-value ratio before liquidation is triggered (Aave ETH: 83-86%).

Liquidation Penalty / Bonus (LB %) 5.0%

Discount given to liquidator seized collateral (standard is 5% to 8%).

Pool Interest Rate Mechanics

Pool Borrow Utilization Rate (%) 78.0%

Ratio of total borrowed funds to total deposited cash in pool.

Optimal Utilization Kink (U_optimal %) 80.0%

Inflection point where Slope 2 rate multiplier activates.

Emergency Slope 2 Jump Rate (%) 60.0%

Steep marginal rate spike when utilization exceeds the optimal kink.

Simulated Flash Crash Price Shock (%) 0.0%

Stress-test price movement to witness Health Factor decay and liquidation.

Position Health & Solvency HUD RISK RUNTIME

Current Health Factor (HF) 1.30 Safe Zone (> 1.0)

Liquidation Trigger Price $1,882.35 -23.17% Price Buffer

Current Borrow APR 5.40% 3.79% Supply APY (80% Kink)

Protocol Bad Debt Run $0.00 Full Collateral Coverage

Position Balance Sheet & Liquidation Execution Breakdown

Position Metric	Base Metric	Under Shock State	Status / Covenant
Effective Collateral Spot Price	$2,450.00	$2,450.00	0.0% Shock
Gross Collateral Market Value	$245,000	$245,000	100.00 ETH Pledged
Discounted Liquidation Value ($LT \cdot P$)	$208,250	$208,250	85.0% Threshold
Total Outstanding Borrowed Debt	$160,000	$160,000	Principal USDC
Position Health Factor	1.30	1.30	SOLVENT
Liquidator Seizure Call (50% Close Factor)	—	$80,000 Repaid	34.29 ETH Seized
Liquidator Gross Arbitrage Profit (5% Bonus)	—	+$4,000	Instant Flash Loan DEX Arb
Residual Borrower Equity After Liquidation	$85,000	$85,000	0.0% Loss

Stress Matrix: Collateral Price Shock vs. Pool Utilization (HF & Borrow APR)

Quantitative Formulation: Health Factor & Kinked Rate Mechanics

In overcollateralized lending protocols like Aave v3, loan solvency is continuously verified on-chain via decentralized price oracles (Chainlink). When the value of pledged collateral drops relative to debt, liquidation bots monitor the Health Factor threshold.

$$HF = \frac{\sum (C_i \cdot P_i \cdot LT_i)}{D_{\text{total}}} \quad \Longleftrightarrow \quad P_{\text{liquidation}} = \frac{D_{\text{total}}}{C \cdot LT}$$

Where $C$ is collateral units, $P$ is spot price, $LT$ is the asset liquidation threshold (e.g. 0.85), and $D_{\text{total}}$ is aggregate debt. If $HF < 1.0$, liquidators execute liquidation calls up to the Close Factor (typically 50%), receiving collateral discounted by the Liquidation Bonus $LB$.

$$R_{\text{borrow}}(U) = \begin{cases} R_0 + \frac{U}{U_{\text{opt}}} R_1 & U \le U_{\text{opt}} \\[6pt] R_0 + R_1 + \frac{U - U_{\text{opt}}}{1 - U_{\text{opt}}} R_2 & U > U_{\text{opt}} \end{cases}$$

When market runs occur and depositors withdraw capital, pool utilization $U = \text{Borrows} / \text{Deposits}$ exceeds $U_{\text{opt}}$. The steep Slope 2 rate $R_2$ causes borrow APRs to surge exponentially, penalizing leveraged looping and restoring pool liquidity.