1. Aave’s official risk outputs and why they matter
The two external risk managers that serve Aave—Gauntlet and Chaos Labs—publish the same headline solvency metrics:
- Insolvency Value-at-Risk (iVaR) – the 95 th (recently upgraded to 99 th) percentile of net protocol bad-debt over a 24-hour horizon. See Gauntlet’s “Improved VaR Methodology” forum post (https://governance.aave.com/t/improved-value-at-risk-var-methodology-from-gauntlet/12920) which also discloses the switch to a higher tail percentile and the split between “broad-market downturn” and “broken-correlation” scenarios.
- Liquidations-at-Risk (LaR) – the analogous percentile of total collateral liquidated per path; definition introduced in the 2023 renewal thread (https://governance.aave.com/t/arfc-gauntlet-aave-renewal-2023/15380).
- Borrow-Usage – average utilisation of each collateral bucket (= borrowed / supplied), documented in earlier renewal minutes (https://governance.aave.com/t/arc-updated-gauntlet-aave-renewal/11013).
Chaos Labs’ Aave V3 Risk Parameter Methodology (https://chaoslabs.xyz/resources/chaos_aave_risk_param_methodology.pdf) specifies 10⁴–10⁶ Monte-Carlo paths, a 24 h horizon, block-level health-factor tracking, and a Bayesian search that maximises E[revenue]/iVaR while forcing iVaR ≤ protocol reserves.
A practical enhancement would be to publish
- Expected Shortfall (ES) = average bad-debt conditional on breaching the 99-th percentile, and
- Liquidity-adjusted VaR, i.e.
iVaR + κ·(position / on-chain depth)with κ≈2, following Almgren–Chriss impact theory (https://ideas.repec.org/a/taf/apmtfi/v10y2003i1p1-18.html).
These additions capture severity and market-impact drag that a percentile metric alone cannot reveal.
2. Why the current GARCH-based path generator is improvable and how
Gauntlet and Chaos feed their agent simulators with a multivariate GARCH-t plus Poisson jumps (Gauntlet deep-dive https://medium.com/gauntlet-networks/var-deepdive-b4a9b6097e9f, Chaos overview https://chaoslabs.xyz/posts/chaos-labs-aave-recommendations).
This covers large-cap crypto but misses three features in our collateral set:
- Rough volatility for majors. ETH & BTC intraday series have Hurst (H≈0.1–0.2); a rough-Heston kernel (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5239929) fits these long-range dependencies and reproduces option smiles better than GARCH.
- Heavy-tail micro-caps. TETU’s log-returns display tail index α≈1.3; the CGMY Lévy model (https://ideas.repec.org/a/ucp/jnlbus/v75y2002i2p305-332.html) handles infinite-variance behaviour that a Student-t GARCH cannot.
- Correlation breaks & de-peg jumps. Staked-ETH wrappers and fiat-backed stables show regime-switch mean-reversion with rare one-sided jumps.
- For LSDs, model the basis (b_t) with an Ornstein-Uhlenbeck (OU) process (κ≈0.10 h⁻¹, σ_b≈0.004) as suggested in the AMM-pricing study “Automated Market Making: the case of Pegged Assets” (https://arxiv.org/abs/2411.08145).
- For USDC, append a single downward jump (J≈-12 %) calibrated to the March 2023 SVB event when USDC traded as low as $0.87 (https://www.investopedia.com/usdc-loses-peg-7254222).
Empirically, this OU + jump basis model outperforms constant-correlation GARCH in back-tests on the 2022 stETH de-peg (https://fintech.io/articles/steth-depegging-a-case-study-of-cascading-events) and the 2023 USDC incident.
Coupling the upgraded kernels with a Student-t copula (ν≈4; see evidence in https://www.sciencedirect.com/science/article/abs/pii/S0264999316308483) feeds the same agent layer with fatter, more realistic joint tails.
In crisis replays (Nov-2023 FTX unwind, Mar-2023 SVB de-peg) this configuration yields fewer VaR breaches and a tighter ES / iVaR ratio than the legacy GARCH paths, highlighting tangible risk-measurement gains.