Summary:
Modify the min/max rates of the WETH2-long LlamaLend market on mainnet from 0.1/70% to 0.000031/66%.
Abstract:
Recommendation
We recommend the following parameters for a Semilog implementation:
- rate_min = 3.1e-05
- rate_max = 0.66
We propose a multi-step approach to minimize impact to the market during the transition period.
Transition Management
Stepwise Transition Summary
| Step | α | PredRate@u₀ | PredUtil@r₀ | rate_min | rate_max |
|---|---|---|---|---|---|
| 0 | 0.00 | 0.07361 | 0.66 | 0.001000085307536796 | 0.699988269029062 |
| 1 | 0.33 | 0.05458 | 0.70 | 0.0004422371914120109 | 0.6804324325294998 |
| 2 | 0.67 | 0.03681 | 0.74 | 0.00014604591093805635 | 0.6670950346153229 |
| 3 | 1.00 | 0.02139 | 0.78 | 0.00003058329137253568 | 0.6618875988660429 |
Optimization Analysis:
WETH-long IRM Analysis
Market: WETH-long
Optimal Utilization
To determine a safe utilization ceiling for the WETH market, we analyze user withdrawal behavior during periods of heightened price volatility.
Methodology
- We define volatile periods as days when the oracle price changes exceed 2 standard deviations.
- During these periods, we examine negative asset flows, focusing on the 10th percentile of total asset drawdowns.
- The optimal utilization
u_optis calculated as:
With a conservative safety buffer of 85%, this ensures safety during rapid market shifts.
Results
Yellow markers indicate days of extreme price volatility.
Distribution of withdrawals during volatile periods — the 10th percentile is used to derive u_opt.
Regime
We apply a Z-score-based regime shift detector to identify periods of stable utilization behavior. The algorithm flags a regime once utilization deviates beyond 1.5 standard deviations from a 30-day rolling mean for at least 7 consecutive days.
Detected Regime
- Start: 2025-05-24
- End: 2025-07-17
- Classification: Underutilization compared to target utilization (
u_opt = 0.85)
Z-score signals identify entry into a stable utilization regime.
Utilization distribution within the regime, relative to the 85% optimal threshold.
Experiment
Experiment Context
To estimate the sensitivity of utilization to interest rates, we perform a 2-lag OLS regression using delta_utilization as the dependent variable.
OLS Regression Results
==============================================================================
Dep. Variable: delta_utilization R-squared: 0.077
Model: OLS Adj. R-squared: 0.058
Method: Least Squares F-statistic: 4.063
Date: Thu, 17 Jul 2025 Prob (F-statistic): 0.0493
Time: 16:28:16 Log-Likelihood: 92.500
No. Observations: 51 AIC: -181.0
Df Residuals: 49 BIC: -177.1
Df Model: 1
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------
const 0.0324 0.015 2.178 0.034 0.003 0.062
borrow_apr_lag -0.5637 0.280 -2.016 0.049 -1.126 -0.002
==============================================================================
Omnibus: 15.361 Durbin-Watson: 1.468
Prob(Omnibus): 0.000 Jarque-Bera (JB): 28.042
Skew: 0.840 Prob(JB): 8.14e-07
Kurtosis: 6.221 Cond. No. 49.7
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Moment Matching Validation
We evaluate how well simulated utilization paths reproduce the empirical distribution by comparing the first four moments:
| Moment | Target Value | Simulated Value | Δ (Sim – Target) |
|---|---|---|---|
| Mean | 0.5843 | 0.5769 | -0.0074 |
| Std. Dev. | 0.0627 | 0.0905 | +0.0278 |
| Skewness | 0.6585 | 0.6510 | -0.0075 |
| Kurtosis | 3.5143 | 3.5144 | +0.0001 |
Simulated utilization paths align closely with observed regime dynamics.
Simulated distribution closely matches empirical shape, with slightly higher variance.
IRM Optimization
We optimize the IRM parameters within the identified stable regime, targeting better alignment with utilization dynamics while maintaining robustness.
Methodology
- The optimization minimizes deviation from the target utilization (u_opt = 0.85), time spend in dangerous utilization levels (>=95%) or time spent underutilized (<=55%) and rate volatility over simulated paths.
- We perform multiple optimization runs with different random seeds, selecting the median parameter set for recommendation.
- Performance is evaluated across mean squared error, utilization volatility, and time spent in critical utilization zones.
Optimizer Stability:
Distribution of recommended parameters across 10 independent runs.
Recommended Parameters (Median):
(3.058329137253568e-05, 0.6618875988660429)
Regime Performance Comparison to Current IRM Configurations:
Key Observation:
- MSE: Meaningfully lower compared to production parameters.
- Time Above Threshold: Marginally higher with some paths spending up to 6% of their horizon in 95% utilization or more.
- Time Below Threshold: Meaningfully lower compared to production parameters, with path on average spending between 0 to 20% of the simulated paths below 55% utilization.
- Volatility of Utilization: Marginally lower compared to the current production parameters.
- Volatility of Rate: Marginally higher compared to production parameters and unevenly distributed.
Stress Test
To assess the resilience of the optimized IRM under adverse market conditions, we simulate extreme scenarios by amplifying historical volatility and jump behavior.
Methodology
- Volatility Scaling: Utilization volatility increased by 1.5
- Jump Parameters:
- Jump frequency: 1.5×
- Jump magnitude: 2.0×
- Tail Adjustment: Tail exponent
νreduced to simulate fatter tails
A total of 500 stress paths were simulated using these scaled parameters and the optimized IRM.
Illustrative Scenario on Current IRM
Extreme Scenario Utilization Path
Extreme Scenario Rate Path
Performance Evaluation
Stress scenario metrics confirm the IRM’s robustness, with controlled underutilization and bounded risk at high utilization levels.
Key Observation:
- MSE: The MSE is significantly improved.
- Time Above Threshold: Time above threshold became higher than the current implementation.
- Time Below Threshold: Time below threshold became lower.
- Volatility of Utilization: Remain largely unchanged
- Volatility of Rate: Increases marginally with wider distribution.
Recommendation
We recommend the following parameters for a Semilog implementation:
- rate_min = 3.1e-05
- rate_max = 0.66
Transition Management
Stepwise Transition Summary
| Step | α | PredRate@u₀ | PredUtil@r₀ | rate_min | rate_max |
|---|---|---|---|---|---|
| 0 | 0.00 | 0.07361 | 0.66 | 0.001000085307536796 | 0.699988269029062 |
| 1 | 0.33 | 0.05458 | 0.70 | 0.0004422371914120109 | 0.6804324325294998 |
| 2 | 0.67 | 0.03681 | 0.74 | 0.00014604591093805635 | 0.6670950346153229 |
| 3 | 1.00 | 0.02139 | 0.78 | 0.00003058329137253568 | 0.6618875988660429 |
Specification:
A Semilog monetary policy contract will need deployment, allowing a min rate lower than 0.1%. This will be linked in a reply to this proposal before initiating the vote.