Summary
Recent governance actions, primarily the increased exposure of crvUSD to YieldBasis, have materially changed the crvUSD system: PegKeeper capacity has expanded, mint-market supply dynamics have shifted, and rate volatility has increased as a by-product of more active peg defense.
This proposal evaluates a strategy for reducing rate volatility when minting crvUSD. This involves smoothing the PegKeeper debt fraction portion of the Monetary Policy calculation using an exponential moving average. The aim is to reduce excessive rate volatility without eliminating the rate signals that historically drive borrower behaviour. Changes in crvUSD price are not processed through EMA, maintaining rate responsiveness for direct defense of the peg.
We analyse how different EMA times affect mint-market rate stability, borrower responsiveness, and peg-defense dynamics â backtesting multiple configurations against observed on-chain behaviour and benchmarking resulting volatility against external markets (Aave).
Based on historical borrower behaviour and backtested rate paths, we recommend introducing a 9-day EMA alongside the recently proposed parameter adjustments, acknowledging the explicit trade-off between rate competitiveness and immediate peg defense.
Motivation
Over the past months, crvUSD mint-market rates have exhibited high short-term volatility. Empirically, this volatility is not driven by price deviations, but primarily by rapid changes in PegKeeper debt as a fraction of total system debt.
PegKeepers are working as intended: aggressively defending the peg. However, because PegKeeper debt enters the policy rate directly, this defense effort is transmitted with high sensitivity into mint-market rates.
The result is a system where:
- The peg is tight
- Rates are noisy
- Borrowersâ behaviour is unpredictable
This motivates studying EMA smoothing as a mechanism to separate short-term peg defense from borrower-facing rate signals.
Context: Recent Governance Activity
This analysis builds upon the two recent governance discussions :
- Credit line expansion for Yield Basis â Increased PegKeeper utilisation and debt variability https://gov.curve.finance/t/increase-credit-line-for-yield-basis-to-1b-crvusd/10945
- Adjustment of
targetFractionandrate0â Re-calibration of baseline rates and PegKeeper influence https://gov.curve.finance/t/adjust-parameters-targetfraction-and-rate0-for-crvusd-monetary-policy/10939
The introduction of YieldBasis led to significant short-term volatility in interest rates. The adjustments to targetFraction and rate0 were aimed to counteract that volatility and high rates.
1. Current Interest Rate Model
The current instantaneous interest rate is:
r = \text{rate0} \cdot \exp\!\Big(\tfrac{\text{price\_peg} - \text{price\_crvusd}}{\sigma} - \tfrac{\text{DebtFraction}}{\text{TargetFraction}}\Big)
\text{DebtFraction} = \tfrac{\text{PegKeeperDebt}}{\text{TotalDebt}}
Where:
rate0= base mint-market borrowing rateprice_crvusd= market price of crvUSD- \sigma = sensitivity to peg deviation
TargetFraction= sensitivity to PegKeeper imbalancePegKeeperDebt= total PegKeeper debt outstandingTotalDebt= total crvUSD debt outstanding
Breaking down the two dynamic components:
-
Price Peg Deviation term:
\frac{\text{price}_{\text{peg}} - \text{price}_{\text{crvUSD}}}{\sigma} -
PegKeeper term:
\frac{\text{DebtFraction}}{\text{TargetFraction}}
A visual representation of the model can be found here:
https://crvusd-rate.0xreviews.xyz/
2. Explanation of Each Term
A. Peg Deviation Term: \tfrac{\text{price}_{\text{peg}} - \text{price}_{\text{crvUSD}}}{\sigma}
- If
price < 1: the term is positive â rate increases - If
price > 1: the term becomes negative â rate decreases
This term aims to make borrowing more expensive when crvUSD trades below the peg and cheaper when above it.
B. PegKeeper Imbalance Term: \tfrac{\text{DebtFraction}}{\text{TargetFraction}}
\text{DebtFraction} = \tfrac{\text{PegKeeperDebt}}{\text{TotalDebt}}
- If DebtFraction increases, the rate increases
- If DebtFraction decreases (
pk_debt < target_debt), rate decreases
3. What causes rate volatility on mint market?
We begin to identify why we see very volatile rates on mint markets by breaking down the evolution of each component in the monetary policy over time.
It is notable that the Pegkeeper debt widely fluctuates. Given that it is a direct input to the Monetary Policy, it directly impacts the rate.
To further visualise how much the debt term and price term contribute to the final rate.
From the chart, it is clear that the debt term mostly dominates for the observed period, with occasional spikes of the price term dominating.
Analysis
Since the PegKeeper debt term is the primary driver of rate volatility, we focus our analysis on the effects of smoothing this component. Introducing EMA smoothing creates an explicit trade-off between rate stability and peg responsiveness. If the monetary policy becomes insufficiently responsive to changes in system state, peg stability may weaken; conversely, if it is overly reactive, short-term rate volatility increases. The objective is therefore to identify a balanced regime that mitigates excessive volatility without materially impairing peg defense.
To do so, we proceed in two steps. First, we analyse historical borrower behaviour across nominal rate levels to identify APR regions where minting and repayment activity have been most concentrated. This establishes empirically relevant rate bands in which borrower responses have historically contributed to system rebalancing.
Second, we evaluate how different EMA smoothing horizons affect rate volatility by backtesting alternative window lengths. This allows us to quantify the amount of volatility reduction achieved as the EMA window increases and to identify whether a point of diminishing returns exists beyond which additional smoothing provides limited benefit while further delaying the policy response.
1. Borrower Behaviour Under Different Rate Levels
We begin by examining how mint-market borrowers historically adjust their activity across different borrow-rate levels between 25-Sep-2025 and 30-Nov-2025.
Data: We use transaction-level borrow and repay events, market-level debt and borrowable capacity, and hourly controller APR data from the WBTC-long and WETH-long controllers.
Data Preparation: We align timestamps, forward-fill market aggregates, and normalise repays and borrows by total debt. APR values are computed at each timestamp and discretised into 0.5-percentage-point buckets. Each borrow or repay event is assigned to its corresponding APR bucket and day.
Method: For each day and APR bucket, we aggregate normalised borrow and repay activity to quantify behaviour at each rate level. We then construct APR-by-time heat maps, overlay daily APR paths, and identify rate intervals where borrowers historically borrow most actively or repay most strongly.
Results: Below, we show absolute borrow/repay levels relative to total borrowable/total debt. The following heatmaps show how much of the dayâs total borrowing or repayment activity occurred at different APR levels, with darker colors indicating days and APR buckets with unusually concentrated flows (displayed on a log scale to make differences more straightforward to see). The vertical axis groups events into narrow APR buckets from high to low, while the horizontal axis moves through calendar days. Superimposed on the heatmap is a red line tracing the median APR observed each day, allowing you to see whether actual pricing tended to align with, or diverge from, the APR levels where most activity occurred.
Borrows
Source: Pangea
We observe that for both the WBTC and WETH markets, most borrow transactions in the controller occur when the borrow rate is below 3.25% APR (or below the 3.0% to 3.5% APR bucket).
Repays
Source: Pangea
Furthermore, we see that, for both the WBTC and WETH markets, most repay transactions in the controller occur when the borrow rate is above 11.25% (or above the 11.00%- 11.50% APR bucket).
2. Backtesting EMA Horizons
We next evaluate how alternative monetary-policy specifications would have performed historically by replaying past crvUSD state trajectories and recalculating implied interest-rate paths under different EMA smoothing choices. Importantly, rates act as signals: under alternative configurations, borrowers may have behaved differently, so these backtests represent counterfactual rate paths rather than predictions of actual outcomes.
Data: We queried PegKeeper debt and controller debt from the Curve Prices Database, and aggregate crvUSD price data from Dune. PegKeeper debt and price data are event-driven, whereas controller debt is sampled at 4-hour intervals.
Data Preparation: We unified two event-driven datasets (price and PegKeeper debt), treated the controller debt as non-changing over a 4-hour sample period, standardized timestamps and numeric formats, concatenated all events, sorted them chronologically, and forward-filled missing values.
Note*: The assumption of constant controller debt between 4-hour samples may cause minor deviations between simulated and observed rate values.*
Method: We backtest alternative monetary-policy specifications by replaying historical crvUSD-state trajectories and recomputing implied interest-rate paths under each policy variant. Specifically, we evaluate debt-fraction (pk_debt/total_debt) smoothing across different EMA horizons.
Results: First, we assess whether a 21-day EMA is a viable solution as proposed by Michael Egorov on X.
Our analysis suggests that a 21-day EMA would not have pushed rates into the critical repay bands (above 11.25%), though rates would have fallen low enough to trigger new borrowing. This indicates that a 21-day horizon may be insufficiently responsive to drive deleveraging when needed for peg defense.
To determine a suitable EMA horizon, we quantify how increasing EMA smoothing affects rate volatility, identifying the point of diminishing returns. Smoothing should stabilise rates, but excessive smoothing delays policy response, creating a natural trade-off. We simulated EMA horizons from 0 to 30 days to identify the point of diminishing returns using the Kneedle method. This method identifies the kink in a monotonic curve by finding the point of maximum deviation from a straight line connecting its endpoints. After normalizing both axes, it computes (f(x) - x) and selects the maximum.
The Kneedle method identifies the point of diminishing returns at â 9 days, marking the point where additional EMA smoothing produces rapidly diminishing reductions in rate volatility. A 9-day EMA showed increased variability relative to a 21-day EMA. Regardless, in the regime from 25-Sep-2025 to 30-Nov-2025, it did not reach critical repayment levels, yet exhibited better directional responsiveness toward critical levels.
We extended the analysis with a 4-day EMA to assess whether critical repayment levels were reached during the observed period.
The analysis suggests that a 4-day EMA or lower reaches critical repay levels. We acknowledge that rate swings between 3.25% and 11.25% are not desirable, yet historical behaviour shows that borrowers tend to react most strongly within these bands. Reaching these levels, therefore, ensured that mint-market users contributed meaningfully to peg defenseâprovided the rate accurately reflected underlying system state.
3. Competitiveness Benchmark
To benchmark crvUSD rate volatility against the broader market, we compare it against Aaveâs variable borrow rates for major stablecoins. Note that we use nominal borrow rates without subtracting yield accrued on supplied collateral.
Source: Dune
The table compares daily APR volatility of the mint-market policy rate (under different EMA configurations) against unsmoothed Aave variable borrow rates, asset by asset. Positive values indicate lower volatility than Aave (âless volatileâ), while negative values indicate the policy rate is more volatile than Aave.
Longer EMA horizons meaningfully reduce volatility relative to market benchmarks. In particular, an EMA horizon of 21 days consistently lowers the volatility of the mint-market policy rate relative to Aave across most assets (e.g., DAI +26 %, USDC +9%, USDT +75%), indicating that the policy achieves its intended smoothing effect at sufficiently long horizons.
By contrast, shorter EMA horizons (4 days and 9 days) often keep volatility above Aave levels. This suggests less competitiveness in these markets. The default configuration without EMA smoothing is markedly unstable, exhibiting extreme excess volatility across all assets (ranging from â466% to â954%). An exception is USDT, which displays volatility reductions even at shorter EMA horizons (EMA=4d: +36%; EMA=9d: +61%), likely due to the intrinsically lower variability of Aaveâs USDT borrow rate.
Trade-off Discussion
Introducing an EMA entails a clear trade-off. Smoothing reduces rate responsiveness, diluting mint-market usersâ contribution to immediate peg defense and shifting more of the burden onto PegKeepers to correct short-term deviations.
To put this into perspective, for a 21-day EMA, for a shock to be noticed by the system, this means ~1 week to move halfway, ~2.5 weeks to reach 80%, and ~3.5 weeks to reach 90% of the effect of a permanent shock in pk_debt/total_debt.
Hence, all else equal, we expect a weakening of the pegâs tightness, with delayed support from the mint market users. This may be an acceptable trade-off given that crvUSDâs peg has historically been very tight, and a more stable rate will, overall, increase the value proposition of crvUSD as a product.
As crvUSD total debt grows, PegKeeper debt carries less weight relative to the system debt, resulting in lower rates by construction. This is the same rationale for raising the target debt fraction. The policy compares the PegKeeperâs share of total system debt against a target level through the ratio:
Expanding it gives:
Whenever PegKeeperDebt>TargetFractionâ TotalDebt the ratio exceeds one and it magnifies the negative contribution of the debt term
leading to a lower policy rate. This loosens monetary conditions by lowering borrowing costs and encouraging minting, expanding the crvUSD supply and restoring downward pressure on the peg.
Specification (Proposed Direction)
Our behavioural analysis shows that borrowers predominantly open positions when crvUSD mint rates lie in the ~0.25â3.25% range and repay when rates rise into the 11.25â14.25% band. In backtests from 25-Sep-2025 to 30-Nov-2025, a 21-day EMA on pk_debt/total_debt would not have driven the policy rate into these historically active regions, whereas a 4-day EMA would have.
Quantitatively, a 21-day EMA has a half-life of ~7 days and needs ~17â24 days to transmit 80â90% of a persistent change in PegKeeper debt into the policy rate. Given the observed magnitude and persistence of pk_debt shocks in the tested period, this lag is sufficient to dampen the signal that mint-market users see materially.
From a competitiveness perspective, a 21-day EMA dominates: it consistently delivers smoother rate dynamics than Aave. At the same time, shorter horizons and the default configuration remain more volatile for most assets in our comparison.
We therefore believe:
- A 21-day EMA should be understood as a âPegKeeper-reliantâ regime: it improves the stability of the mint-market rate. Still, it materially weakens the short-term contribution of mint markets to peg defense.
- If the goal is to preserve historical levels of borrower responsiveness, the smoothing horizon should be considerably shorter (e.g., a 4-day EMA) and accompanied by complementary levers (e.g., a steeper rate schedule and more aggressive targetFraction/rate0 parameters) that ensure rates still enter empirically active APR regions under stress.
We recommend:
- To begin with, a 9-day EMA and increase
rate0to 11.55% (3662480974 in raw units) APR. It reduces the volatility compared to the default implementation and comes close to critical repay levels.
Regardless, the trade-off is explicit: more smoothing means greater competitiveness through more predictable rates; less smoothing means a stronger mint-market role in peg defense. Given crvUSDâs historically tight peg, accepting a moderate relaxation of peg tightness in exchange for more stable rates may be an attractive product decision â but it should be made with a clear understanding that a 21-day EMA de-emphasises mint markets as the first line of defense.
Limitation
Borrower reactions are grouped into rate buckets, which may obscure finer behavioural patterns. Findings reflect only the historical period analysed and may not generalise to other market environments. Additionally, rates have been highly volatile (i.e., changing near-instantaneously), which may distort the mapping between observed rates and effective borrower decision points.
Backtesting results rely on reconstructed on-chain data, including the assumption that controller debt remains constant between 4-hour snapshots. Importantly, rates act as signals: under alternative configurations, borrowers would have responded differently, altering the very inputs to the monetary policy. These second-order effects have not been accounted for.
The study assumes historical borrower behaviour will persist, but this may not hold. In practice, reduced rate volatility could itself change borrower patterns â given time, rates should converge around a market average, and tighter oscillations around that average would likely attract more borrowers overall.
Next Steps
Finally, implementation of these changes is contingent on the completion of the updated monetary policy contract, which is currently under development in collaboration with Swiss Stake and LlamaRisk. Once the contract is finalised and deployed, the configuration discussed in this post will be applied at deployment using the parameters specified herein.