Introduction
Source Study: [_DeFi Risk Assessment: MakerDAO Loan Portfolio Case_]
Objective: To evaluate risk exposure in MakerDAO's lending portfolio.
Core Methodology: Development of a multi-asset risk model based on Brownian motion thresholds—where price fluctuations of collateral types are modeled as correlated Brownian motions, with channel levels corresponding to users' collateralization ratios.
Significance
This study delivers a pioneering risk assessment framework for DeFi lending platforms. By integrating collateral price correlations and liquidation thresholds, the model enhances epochChain's research on fraud token detection and lays groundwork for developing secure altcoin lending systems.
1. Background: MakerDAO Protocol
Core Mechanics
- DAI Stablecoin: An ERC-20 token pegged to USD, generated via Collateralized Debt Positions (CDPs) in "Vaults" where users lock crypto assets (e.g., ETH, WBTC).
- Governance: Parameters (e.g., stability fees, liquidation ratios) are voted on by MKR token holders through decentralized governance.
Borrower Workflow
- Deposit collateral into a Vault (e.g., ETH-A/B/C).
- Generate DAI up to the collateral value × loan-to-value (LTV) ratio.
- Repay DAI + fees to unlock collateral; failure triggers liquidation (10–33% penalty).
Key Innovation: Autonomous liquidations via smart contracts minimize human intervention.
2. Literature Review
Traditional Finance vs. DeFi
| Aspect | Traditional Finance | DeFi (MakerDAO) |
|----------------------|-----------------------------------|-------------------------------|
| Risk Models | Basel III, ML (random forests) | On-chain data, Brownian motion|
| Data Access | Proprietary | Transparent blockchain records|
Research Gap: Existing DeFi models lack granularity in:
- Multi-collateral default correlations.
- Quantifying joint liquidation risks.
3. Mathematical Model
3.1 Key Variables
| Symbol | Description |
|---------|--------------------------------------|
| ( t ) | Loan duration |
| ( m ) | Number of collateral assets |
| ( \rho_{ij} ) | Correlation between assets (i) and (j) |
3.2 Default Probability (Theorem 1)
Assumptions:
- Asset prices follow geometric Brownian motion: ( dS_i/S_i = \mu_i dt + \sigma_i dW_i ).
- Zero interest rates (valid approximation for MakerDAO’s 1–5% stability fees).
Joint Default Formula:
For two assets with correlation ( \alpha ):
[ P(\tau_1 \leq T, \tau_2 \leq T) = \int_{-\infty}^{b_1} \int_{-\infty}^{b_2} f_{W_1,W_2}(w_1,w_2) \, dw_1 dw_2 ]
where ( b_i = \ln(\text{LTV threshold}) ).
3.3 Portfolio Risk (Theorem 2)
Extends Theorem 1 to ( m ) assets, computing the probability distribution of total protocol-wide liquidation value.
Key Output:
CCDF of liquidation amounts informs risk reserves.
4. Numerical Experiments
4.1 Synthetic Data
Finding 1: BTC-ETH price increments show strong correlation (( \alpha = 0.8 )), validating Brownian motion coupling.
Finding 2: Zero-rate assumption introduces <1% error vs. Monte Carlo simulations.
👉 Explore real-time crypto correlations
4.2 Real-World Data (2019–2023)
| Asset | Model MSE (Brownian) |
|---------|----------------------|
| ETH-A | 0.047 |
| WBTC-A | 0.051 |
Cross-Asset Risk: ETH-A + WBTC-A joint default probability rises 30–50% over 1-year vs. 1-day horizons.
5. Conclusions
- Effectiveness: The model successfully quantifies multi-collateral risks in MakerDAO.
- Limitations: Assumes continuous price paths; real-world jumps (e.g., crypto crashes) may require Poisson adjustments.
Future Work: Incorporate machine learning for dynamic threshold calibration.
FAQ
Q1: How does MakerDAO’s liquidation mechanism reduce risk?
A: Automated smart contract liquidations ensure rapid debt coverage, minimizing protocol losses.
Q2: Why model interest rates as zero?
A: Stability fees (1–5%) contribute minimally to short-term default probabilities vs. price volatility.
Q3: Can this model apply to Aave or Compound?
A: Yes, but protocol-specific parameters (e.g., LTV curves) must be adjusted.