3 Key Insights: Why LST Collateral Requires Different CDP Parameters

LST collateral risk is well understood conceptually, but parameter optimization is still challenging. How much should liquidation ratios increase for stETH vs rETH? What's the optimal oracle window for different market conditions? When does correlation risk justify higher capital requirements?

The May 2022 Terra collapse demonstrated these challenges in practice - stETH depegs triggered liquidation cascades in Aave and Compound that exceeded what traditional risk models predicted. At CryptoEconLab, we've built mathematical frameworks to solve these parameter optimization problems.

Our interactive stETH depeg simulator demonstrates quantitative approaches to LST risk management. Here are three key insights from our modeling:

Key Insights Summary

Insight 1: LST Collateral Has Dual Risk Dimensions

Unlike native ETH collateral which only faces price volatility, LST collateral faces two independent risk sources: ETH price movements AND depeg risk. When ETH crashes, your ETH collateral loses value. When stETH depegs, your stETH collateral faces an additional loss on top of any ETH price decline. This creates a different risk profile that traditional CDP parameters don't account for.

Insight 2: Traditional Parameters Are Insufficient During Correlated Events

The May 2022 Terra collapse revealed the danger of correlated risk events where ETH price crashes coincide with LST depegs. ETH fell 29% while stETH simultaneously depegged to 0.94 ETH, creating a compound loss that liquidated even conservatively collateralized positions. Traditional risk models treat these as independent events which can underestimate liquidation probability during market stress.

Insight 3: Risk Management Requires Fundamental Trade-offs

Every approach to managing LST collateral risk involves unavoidable trade-offs. Higher liquidation ratios reduce liquidation risk but decrease capital efficiency. Faster oracles prevent bad debt but increase false liquidation risk. Moving average oracles reduce false liquidations but allow bad debt accumulation during real depeg events. Protocols must explicitly choose which risks to prioritize.

Relatedly, a protocol can decide to "wait out" the depeg rather than liquidate, since LSTs have fundamental backing. However, this approach transfers market risk from borrowers to the protocol. More concretely, even if the LST peg recovers perfectly, price decline of the underlying during the waiting period can still create bad debt scenarios.

Recommendations for DeFi Protocols

1. Asset-Specific Parameters

Implement risk-adjusted liquidation ratios that account for both depeg risk and the historical correlation between ETH price movements and LST depegs for each specific asset.

2. Dynamic Risk Management

Monitor real-time correlation between ETH price and LST ratios. During periods of high positive correlation (market stress), automatically increase liquidation ratios and depeg tolerance parameters.

3. Oracle Hybrid Approach

Use responsive oracles during normal market conditions but automatically extend averaging windows during high volatility periods to balance responsiveness with stability.

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Mathematical Framework

This section provides the detailed mathematical analysis underlying the insights above.

The Dual Risk Mathematical Model

Native Token Collateral operates with a single risk dimension:

$\text{ETH}_{\text{Value}}(t) = \text{Amount} \times \text{ETH}_{\text{Price}}(t)$

The ETH/ETH ratio is always 1.000, meaning no depeg risk exists.

LST Collateral introduces a second risk dimension:

$\text{LST}_{\text{Value}}(t) = \text{Amount} \times \text{ETH}_{\text{Price}}(t) \times \text{LST/ETH}_{\text{Ratio}}(t)$

Since LST value depends on both ETH price and the LST/ETH ratio, we can approximate the total returns as:

$\text{LST}_{\text{Return}} \approx \text{ETH}_{\text{Price-Return}} + \text{LST/ETH}_{\text{Ratio-Return}}$

$\text{LST}_{\text{Return}} = R_{\text{price}} + R_{\text{depeg}}$

This creates two sources of risk using the variance formula:

$\text{Risk}_{\text{LST}} = \text{Var}(R_{\text{price}} + R_{\text{depeg}})$

$\text{Risk}_{\text{LST}} = \sigma_{\text{price}}^2 + \sigma_{\text{depeg}}^2 + 2\rho \times \sigma_{\text{price}} \times \sigma_{\text{depeg}}$

Where:

• $\sigma_{\text{price}}^2$ = ETH price volatility (affects both ETH and LST collateral)
• $\sigma_{\text{depeg}}^2$ = LST depeg volatility (only affects LST collateral)
• $2\rho \times \sigma_{\text{price}} \times \sigma_{\text{depeg}}$ = correlation term (amplifies risk when $\rho > 0$)

The additional risk from using LST instead of ETH is:

$\text{Additional}_{\text{Risk}} = \sigma_{\text{depeg}}^2 + 2\rho \times \sigma_{\text{price}} \times \sigma_{\text{depeg}}$

Note on LST Yield: LSTs do accrue staking rewards over time (~4% annually), which provides a small positive drift to collateral value. However, this yield is negligible compared to depeg risk during crisis periods. A high single-digit or low double digit depeg can occur in days and overwhelm months of yield accumulation. For risk management purposes, the yield component doesn't materially change liquidation ratio requirements during stress scenarios.

Liquidation Condition Mathematics

For any CDP, liquidation occurs when:

$\text{Collateral}_{\text{Ratio}}(t) = \frac{C \times \text{ETH}_{\text{Price}}(t) \times \text{LST/ETH}_{\text{Ratio}}(t)}{D} < \text{Liquidation}_{\text{Ratio}}$

Rearranging, liquidation occurs when:

$\text{ETH}_{\text{Price}}(t) \times \text{LST/ETH}_{\text{Ratio}}(t) < \frac{D \times \text{Liquidation}_{\text{Ratio}}}{C}$

May 2022 Example: With 150% liquidation ratio:

• ETH price declined 29% (to 0.71)
• stETH/ETH ratio fell to 0.94
• Combined effective threshold: $150\% \times 0.71 \times 0.94 = 100.2\%$

Even conservatively collateralized positions faced liquidation.

Depeg Progression Model

Our simulator models depeg events using an S-curve that captures real-world LST depeg dynamics:

$R(t) = R_{\text{min}} + (1 - R_{\text{min}}) \times (1 - S(t)) + \varepsilon(t)$

Where: $S(t) = \frac{1}{1 + \exp(-0.2 \times (t-23))}$

The S-curve captures three phases:

1. Initial stress (hours 0-20): Small depeg as first movers exit
2. Acceleration (hours 20-40): Rapid depeg as liquidity dries up
3. Stabilization (hours 40+): New equilibrium based on fundamental backing

Parameter Optimization

The capital efficiency trade-off can be expressed as:

$LR_{\text{optimal}} = \arg\min[w \times P_{\text{liquidation}}(LR) + (1-w) \times \frac{1}{\text{Capital}_{\text{Efficiency}}(LR)}]$

Asset-specific liquidation ratios:

$LR_{\text{asset}} = LR_{\text{base}} \times (1 + \alpha \times (1 - R_{\text{min}}) + \beta \times \sigma_{\text{correlation}})$

Dynamic correlation monitoring:

$\rho_{\text{rolling}} = \text{Correlation}(R_{\text{ETH}}[t-30:t], R_{\text{depeg}}[t-30:t])$

$\delta(\text{market}_{\text{stress}}) = \delta_{\text{base}} \times (1 + \beta \times |\rho_{\text{rolling}}|)$

Oracle hybrid approach:

$\text{Oracle}_{\text{Window}} = \text{Base}_{\text{Window}} \times (1 + \gamma \times \text{Volatility}_{\text{Regime}})$

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Takeaways

LST collateral introduces mathematically quantifiable additional risk through both pure depeg events and correlation effects during market stress. The May 2022 Terra collapse demonstrated how positive correlation can amplify losses beyond what either risk dimension would cause alone. Protocols must use rigorous mathematical modeling to set appropriate parameters, accounting for the full spectrum of risk scenarios from isolated depegs to compound market crises.

The dual-dimensional risk profile of LST collateral - combining price volatility with depeg risk - requires fundamentally different parameter design than traditional ETH-based CDP systems. Our mathematical framework provides the tools for quantifying these risks and optimizing protocol parameters accordingly.

In the future, we aim to conduct a more complete analysis that will compare the expected value of annual yield versus the expected annual losses from depeg events (accounting for frequency, magnitude, and recovery patterns). This probabilistic framework could refine optimal parameter settings beyond crisis-focused models.

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Want to explore these risks interactively? Try our stETH Depeg Simulator to see how isolated depeg events compare to compound crisis scenarios.