Decentralized Finance (DeFi) has revolutionized traditional lending by enabling trustless, transparent, and automated borrowing through smart contracts. At the forefront of this innovation stands MakerDAO, a pioneering protocol on the Ethereum blockchain that issues DAI, a dollar-pegged stablecoin, through collateralized debt positions (CDPs). As DeFi ecosystems grow in complexity and scale, so does the need for robust risk assessment models—especially when users can deposit multiple asset types as collateral.
This article presents a comprehensive risk evaluation framework for MakerDAO’s multi-collateral loan portfolio, leveraging stochastic modeling to quantify default probabilities and portfolio-level risks. By integrating mathematical rigor with real-world data validation, the model offers actionable insights for developers, researchers, and risk analysts working in DeFi.
Core Keywords
- MakerDAO
- DeFi risk assessment
- Multi-collateral loans
- Brownian motion modeling
- Joint default probability
- Loan portfolio risk
- Cryptocurrency volatility
- Smart contract lending
Background: Understanding MakerDAO's Lending Mechanism
MakerDAO operates as a decentralized autonomous organization (DAO), where governance token holders vote on key parameters such as stability fees and liquidation ratios. Users generate DAI by locking crypto assets—like ETH or WBTC—into smart contract vaults. The amount of DAI they can mint depends on the collateral's value, determined via decentralized oracles.
Each collateral type follows specific risk parameters under distinct vault categories (e.g., ETH-A, WBTC-A), including:
- Minimum collateralization ratio (typically 150%)
- Stability fee (interest rate)
- Liquidation penalty (10%–33%)
If the collateral value drops below the required threshold, the vault is automatically liquidated: the system auctions off the collateral to repay the debt. Any shortfall is absorbed by the protocol, making accurate risk forecasting critical to financial stability.
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Related Work: Bridging Traditional Finance and DeFi Risk Models
Traditional finance employs regulatory standards like Basel III and statistical tools such as linear regression or random forests to assess credit risk. However, these models rely on private data and often lack transparency.
In contrast, DeFi’s open blockchain architecture provides full access to transactional data, enabling novel analytical approaches. Prior studies have explored DAI stability, single-asset default modeling, and portfolio diversification in protocols like Compound and Aave. Yet, most fail to account for inter-asset correlations—a crucial factor when ETH and WBTC move in tandem during market shocks.
This study fills that gap by introducing a multi-asset joint default model based on correlated Brownian motions—a first in DeFi risk quantification.
Mathematical Framework: Modeling Risk with Stochastic Processes
3.1 Key Variables and Assumptions
The model defines several core components:
- Time horizon: From loan initiation to repayment, liquidation, or maximum observation window.
- Collateral dynamics: Asset prices evolve according to geometric Brownian motion.
- Debt accumulation: Debt grows exponentially at a fixed interest rate.
- Oracle pricing: Real-time exchange rates feed into collateral ratio calculations.
- Liquidation trigger: Occurs when the current collateralization ratio falls below the minimum threshold.
Let $ X_t^{(i)} $ represent the logarithmic price of asset $ i $, modeled as a Brownian motion:
$$ dX_t^{(i)} = \sigma_i dW_t^{(i)} $$
where $ W_t^{(i)} $ is a Wiener process.
3.2 Joint Default Probability: Theorem 1
Defining Default
A default event occurs when a vault’s collateral ratio breaches its liquidation level—mathematically equivalent to a Brownian path crossing a lower boundary.
For two assets, we define:
- $ T_1 $: First passage time of asset 1 to its threshold
- $ T_2 $: First passage time of asset 2 to its threshold
The joint default probability within time $ T $ is:
$$ P(T_1 \leq T, T_2 \leq T) $$
Correlation Structure
To capture co-movement between assets (e.g., ETH and WBTC), we model the second asset’s motion as a linear combination:
$$ W_t^{(2)} = \alpha W_t^{(1)} + \sqrt{1 - \alpha^2} Z_t $$
where $ Z_t $ is an independent Brownian motion and $ \alpha \in [0,1] $ reflects correlation.
Using results from Zhou (2001) on correlated first-passage times, the joint probability is derived via double integrals involving modified Bessel functions.
Model Implications
This framework allows us to:
- Quantify how correlated volatility increases systemic risk
- Estimate cascading liquidations across asset classes
- Inform dynamic risk parameter adjustments
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3.3 Portfolio-Level Risk: Theorem 2
Extending Theorem 1 to $ m $ assets, we compute the probability distribution of total liquidation value across all vaults.
Assume:
- Each asset has $ n_i $ users ranked by risk (lowest collateral ratio first)
- Users do not adjust positions during observation period
Then, the probability that the total defaulted debt exceeds amount $ L $ is:
$$ P\left(\sum_{i=1}^m S_i \geq L\right) = \sum_{\text{combinations}} P(\text{joint default of selected users}) $$
where $ S_i $ is the sum of debts from defaulted users in asset class $ i $.
This enables:
- Estimation of worst-case loss scenarios
- Capital reserve planning
- Stress testing under extreme market conditions
Numerical Validation: Synthetic and Real-World Data Experiments
4.1 Synthetic Data Testing
Normality and Correlation Analysis
Shapiro-Wilk tests on BTC price increments show deviations from normality (p < 0.05), yet Brownian motion remains a viable approximation for medium-term forecasting.
Cross-asset correlation between BTC and ETH ranges from 0.79 to 0.84, supporting the linear combination assumption.
Zero-Rate Approximation Test
Monte Carlo simulations confirm that assuming zero interest introduces negligible error (RMSE < 0.01) even at real-world rates (1%–5%), validating model tractability.
Risk Distribution Output
Complementary Cumulative Distribution Functions (CCDFs) for a 20-user dual-asset system show exponential growth in default likelihood as collateral thresholds decrease—aligning closely with theoretical predictions.
4.2 Real Data from MakerDAO (2019–2023)
Using Google BigQuery data from November 2019 to July 2023:
- Analyzed ETH-A, WBTC-A, GUNIV3DAIUSDC2-A vaults
- Tracked debt levels, collateral prices, and liquidation events
Model Comparison: Brownian vs. Poisson
| Asset | MSE (Brownian) | MSE (Poisson) |
|---|---|---|
| ETH-A | 0.047 | 0.048 |
| WBTC-A | 0.061 | 0.052 |
Brownian motion outperforms Poisson for ETH-based vaults due to smoother price trends; Poisson better captures Bitcoin’s jump risks.
Multi-Asset Joint Default Trends
Over increasing time horizons:
- 1-day P(default ≥ x): ~5%
- 1-year P(default ≥ x): ~35%
This confirms that longer exposure significantly raises systemic risk—a vital insight for protocol designers.
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Conclusion: Advancing DeFi Risk Science
This study introduces a novel multi-collateral risk assessment model for MakerDAO using correlated Brownian motion to estimate joint default probabilities and portfolio loss distributions. It advances prior work by:
- Incorporating inter-asset dependencies
- Providing closed-form solutions for dual-assets
- Scaling to multi-user, multi-asset portfolios
While assumptions like constant rates and no user intervention limit real-time accuracy, numerical experiments confirm strong predictive power—especially for long-term risk trends.
Future directions include:
- Integrating jump-diffusion processes for black-swan events
- Adding behavioral modeling (user top-ups, withdrawals)
- Applying machine learning for dynamic parameter calibration
As DeFi evolves, project-specific risk models will become essential for sustainability. This framework lays the groundwork not only for MakerDAO but also for Aave, Compound, and emerging lending protocols navigating an increasingly interconnected digital asset landscape.
Frequently Asked Questions (FAQ)
Q: What makes this model different from traditional credit risk models?
A: Unlike bank-centric models relying on credit scores and private data, this approach uses public blockchain data and stochastic price modeling to assess default risk in real time—tailored specifically for over-collateralized crypto loans.
Q: Why use Brownian motion if crypto prices aren't perfectly normal?
A: While crypto returns exhibit fat tails and jumps, Brownian motion provides a mathematically tractable baseline for medium-term risk projection. It balances simplicity with sufficient accuracy when validated against historical data.
Q: Can this model predict flash crashes?
A: Not directly. The current version assumes continuous price paths. To model flash crashes, future iterations should incorporate jump-diffusion or Levy processes.
Q: How can protocols use this model practically?
A: Teams can use it to set dynamic liquidation ratios, calculate required insurance funds, simulate stress scenarios, and optimize collateral types based on correlation profiles.
Q: Is the model applicable beyond MakerDAO?
A: Yes. The core methodology—modeling multi-collateral defaults via correlated stochastic processes—can be adapted to any over-collateralized lending platform in DeFi.
Q: Does high correlation between ETH and WBTC increase systemic risk?
A: Absolutely. Strong positive correlation means both assets may decline simultaneously during market downturns, increasing the chance of widespread liquidations—a key finding confirmed by this model.