Introduction

In Traditional Finance, credit is based on Trust (FICO Score). In DeFi, credit is based on Physics (Over-Collateralization).

The protocol does not trust you. It trusts the Liquidation Engine. If your Health Factor drops below 1.0000, a bot will instantly seize your collateral, sell it at a discount, and pay off your debt. This lesson explores the ruthless math that keeps DeFi solvent.

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The Physics: Health Factor ($H_f$)

You deposit ETH. You borrow USDC. When do you die?

$H_f = \frac{\sum (Collateral_i \times Threshold_i)}{Total Debt}$

• Collateral: $1000 ETH.
• Liquidation Threshold ($L_t$): 80% (0.8).
• Borrowing Power: $800 USDC.
• Total Debt: $500 USDC.
• Result: $H_f = \frac{1000 \times 0.8}{500} = 1.6$.

Physics: If $H_f < 1.0$, you are insolvent relative to the protocol’s risk parameters. Liquidation is essentially instantaneous.

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Deep Dive: The Interest Rate Model (The Kink)

Why do stablecoin rates spike to 50%? Because of the Utilization Rate ($U$).

$U = \frac{Total Borrows}{Total Liquidity}$

The Interest Rate curve has a “Kink” at an optimal point (usually 80% or 90%).

• Below Kink: Rates are low (slope is gentle). Encourages borrowing.
• Above Kink: Rates shoot to infinity (slope is steep). Encourages repayments.

Physics of the Kink: If $U$ hits 100%, lenders cannot withdraw. The protocol is insolvent (Bank Run). The Kink is a defense mechanism to force borrowers to repay before the pool runs dry.

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The Mechanism: Liquidation Engines

How does Aave sell your collateral? It doesn’t use an Order Book. It offers an Arb Opportunity.

Fixed Spread Liquidation (Aave V2):

1. Your Debt: $100 USDC.
2. Your Collateral: $110 ETH.
3. Bonus: Protocol offers your ETH to liquidators at a 5% discount.
4. Liquidator: Pays $100 USDC. Receives$105 worth of ETH. Profits $5 instantly.

Dutch Auction (MakerDAO): Protocol slowly lowers the price of your collateral until a bidder steps in.

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Code: Interest Accrual (Index Math)

Interest is not calculated per second per user (too much gas). It is calculated using a global Liquidity Index.

def accrue_interest(pool, current_time):
    time_delta = current_time - pool.last_update_time
    rate = pool.current_interest_rate
    
    # Simple Interest Factor for this period
    interest_factor = rate * time_delta
    
    # Update Global Index
    # Index grows like: 1.0 -> 1.01 -> 1.0201 ...
    pool.liquidity_index = pool.liquidity_index * (1 + interest_factor)
    pool.last_update_time = current_time

def get_user_balance(user, pool):
    # Principal * (CurrentIndex / UserIndex)
    growth = pool.liquidity_index / user.last_index
    return user.principal_balance * growth

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Practice Exercises

Exercise 1: The Margin Call (Beginner)

Scenario: ETH $2000. L_t 80$1000 USDC. Task: At what ETH price does $H_f = 1.0$? (Answer: $Price \times 0.8 = 1000 \rightarrow Price = 1250$).

Exercise 2: The Spiral (Intermediate)

Scenario: A Whale is liquidated. The liquidator sells the ETH on Uniswap. Task: What happens to the ETH price? (Drops). What happens to your Health Factor? (Drops). This is a Liquidation Cascade.

Exercise 3: Utilization Spike (Advanced)

Scenario: $U$ jumps from 80% to 95%. Task: Calculate the new APR if the slope after the Kink is 100%. (Rates might jump from 4% to 50% instantly).

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Knowledge Check

1. What does a Health Factor of 1.1 mean?
2. Why does the Interest Rate curve have a Kink?
3. Who executes liquidations?
4. Why is “Isolation Mode” safer for new assets?
5. Does the protocol hold your tokens?

Answers

1. Safety. You are 10% away from liquidation.
2. Liquidity Risk. To prevent 100% utilization (Bank Run) by making borrowing painfully expensive.
3. Third-party Bots. They are incentivized by the liquidation bonus.
4. Contagion Control. Borrowing against a risky asset shouldn’t threaten the solvency of the main USDC pool.
5. Yes. But they are usually wrapped in aTokens/cTokens which represent your claim on the pool.

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Summary

• HF < 1: Death.
• Kink: The line between cheap leverage and liquidity crisis.
• Liquidators: The immune system of DeFi.

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