From Interest Rates to Liquidation Fees A Complete DeFi Modeling Guide

The Journey From Interest Rates to Liquidation Fees: A Complete DeFi Modeling Guide

In the fast‑moving world of decentralized finance, every token holder, liquidity provider, and protocol architect depends on a clear mathematical framework. Interest rates determine how much borrowers pay, while liquidation fees and bonuses protect the system’s solvency. Together, these variables form a complex yet structured ecosystem that can be modeled, analyzed, and optimized. This guide walks you through the key concepts, demonstrates how to translate them into equations, and gives a step‑by‑step tutorial for building a robust DeFi borrowing model.

The Building Blocks of DeFi Lending

1. Interest Rate Fundamentals

Interest rates in DeFi are typically expressed as an annual percentage yield (APY), derived from a daily or hourly compounding process—a topic also covered in depth in the article on Interest Rate Dynamics and Borrowing Strategies in DeFi Platforms. Two core components shape the APY:

• Base Rate: Often set by protocol governance or algorithmic rules, it represents the risk‑free portion of the yield.
• Liquidity Incentive: A dynamic factor that rewards lenders when the market is under‑funded and punishes them when the market is over‑funded.

The interest formula for a borrower’s debt D over a time interval Δt (in days) can be written as:

D(Δt) = D0 × (1 + r_daily)^Δt

Where r_daily is the daily interest rate (APY / 365). The daily rate is itself a function of the current utilization u of the pool:

r_daily(u) = base_rate_daily + liquidity_incentive(u)

2. Borrowing Mechanics and Collateralization

Borrowers must supply collateral to access credit. Two key ratios govern this process:

• Loan‑to‑Value (LTV): Maximum permissible borrowing expressed as a percentage of the collateral’s market value.
• Liquidation Threshold (LT): When the collateral’s value falls below this percentage relative to the outstanding debt, the position becomes eligible for liquidation.

For a collateral amount C priced at P_C, the maximum borrowable amount is:

MaxBorrow = C × P_C × LTV

The health factor (HF) is the ratio of the current collateral value to the debt required to trigger liquidation:

HF = (C × P_C × LT) / D

If HF < 1, the position can be liquidated.

Dynamic Interest Rate Models

Protocols employ several mathematical models to keep rates responsive:

Choosing a model depends on the protocol’s risk appetite and market conditions; see Optimizing Liquidation Penalties and Incentive Structures in DeFi for how these choices affect overall risk.

Liquidity Pools and Interest Calculation

Liquidity pools gather supplied assets into a single fund. The pool’s utilization u is defined as:

u = TotalBorrowed / TotalSupplied

When u rises, the supply side sees a higher incentive, and the borrow side sees a higher cost. This feedback loop is essential for self‑balancing markets.

Daily Compound Example

Assume a pool with:

• Total supplied: 1,000,000 USDC
• Total borrowed: 400,000 USDC
• Base rate: 0.5% APY
• Liquidity incentive: 1% APY when u > 0.5

u = 0.4, so the incentive is not triggered. Borrowers pay:

APY = 0.5%
Daily rate = 0.5% / 365 ≈ 0.00137%

If the pool grows to 800,000 USDC borrowed:

u = 0.8 → Incentive applies
APY = 0.5% + 1% = 1.5%
Daily rate = 1.5% / 365 ≈ 0.00411%

Risk Parameters: LTV, Liquidation Threshold, and Liquidation Bonus

Typical values for these parameters are also explored in Building a Robust DeFi Financial Model for Borrowing and Liquidation.

Liquidation Process

1. Trigger: HF < 1.
2. Liquidator Action: Repays part or all of the borrower’s debt.
3. Reward: Receives a portion of the collateral plus the bonus.
4. Collateral Transfer: Remaining collateral is redistributed to the pool.

The liquidation penalty ensures that borrowers are incentivized to maintain healthy collateral levels, while the bonus compensates liquidators for their effort.

Modeling Liquidation Fees and Penalties

The liquidation fee can be derived from the difference between the collateral value and the debt amount at the moment of liquidation. For a debt D, collateral value C_val, and bonus b, the fee F is:

F = (C_val × (1 + b)) - D

The derivation follows the principles outlined in The Mathematics Behind DeFi Borrowing and Liquidation Incentives.

If F is negative, the borrower still has a shortfall; if positive, the liquidator has profited. In most protocols, the fee is capped to prevent excessive payouts.

Example

• Debt: 200 USDC
• Collateral value at liquidation: 250 USDC
• Bonus: 10%

F = (250 × 1.10) - 200 = 275 - 200 = 75 USDC

The liquidator receives 75 USDC, which is 37.5% of the initial collateral value.

Step‑by‑Step Guide to Building a DeFi Borrowing Model

1. Define Input Variables

• Market price of collateral (P_C)
• Total supplied (S)
• Total borrowed (B)
• Base interest rate (r_base)
• Liquidity incentive function (r_incentive(u))
• LTV (LTV)
• Liquidation threshold (LT)
• Liquidation bonus (b)

2. Compute Utilization

u = B / S

3. Calculate Daily Interest Rate

r_daily = (r_base + r_incentive(u)) / 365

4. Update Borrowed Amount

B_new = B × (1 + r_daily)

5. Determine Health Factor

HF = (C × P_C × LT) / B_new

6. Check for Liquidation

If HF < 1, compute liquidation fee:

C_val = C × P_C
F = (C_val × (1 + b)) - B_new

7. Update Pool Balances

• If liquidation occurs, reduce C by the portion sold to liquidator.
• Adjust S and B accordingly.

8. Iterate Over Time

Repeat steps 2–7 daily or hourly to simulate the pool’s evolution.

Practical Example: Aave v2 Model

Aave v2 uses a stable‑rate and a variable‑rate borrowing mode. For the variable mode, the model is:

r_variable = r_base + k × u

Where k is a protocol‑specific constant that increases with utilization. For the stable mode, the rate is capped at a maximum stable rate to provide predictability.

Liquidation Conditions in Aave

• Borrower’s Health Factor = (Collateral Value × LT) / Borrowed Amount
• Minimum Health Factor to avoid liquidation: 1.0
• Liquidation Bonus: 0.08 (8%) for ERC‑20 tokens

Implementing Aave’s exact formulas requires access to the protocol’s contract data, but the general structure follows the guide above.

Sensitivity Analysis

Understanding how changes in key parameters affect outcomes is essential for risk management, as discussed in DeFi Risk Management Through Advanced Interest Rate and Liquidation Models.

• Impact of LTV: Raising LTV increases borrowing power but lowers the buffer before liquidation.
• Effect of Liquidation Bonus: A higher bonus attracts more liquidators but reduces the protocol’s margin.
• Utilization Threshold: Lower thresholds trigger more frequent liquidations, tightening liquidity but enhancing safety.

Run simulations varying each parameter to see the effect on pool health, borrower payoff, and protocol revenue.

Visualizing the Model

Below is a conceptual diagram that shows how rates adjust with utilization and how liquidation flows through the system.

Common Pitfalls and How to Avoid Them

Conclusion

DeFi lending combines straightforward financial concepts with sophisticated mathematical modeling. By carefully defining interest rates, collateral parameters, and liquidation mechanics, one can build a transparent, predictive model that serves both borrowers and protocol designers. The step‑by‑step framework outlined above is adaptable to any DeFi platform, whether it follows Aave’s design, Compound’s proportional model, or a custom protocol’s logic.

With this guide, you now have a solid foundation to build, test, and refine a DeFi borrowing model that balances profitability, risk, and user experience. Happy modeling!