verex

AMM curve slippage simulation — decision support (2026-08-03)

Source feature doc: docs/features/hybrid-amm-clob.md (“Extreme-probability handling” — its first dev item asks for exactly this simulation before the curve is locked in). Script: packages/api/scripts/sim-amm-slippage.ts — rerun with pnpm --filter @verex/api exec tsx scripts/sim-amm-slippage.ts.

Setup (comparable by construction)

• CPMM (x·y=k) and StableSwap (Curve n=2, A=10, value-normalized so the flat region sits at the current spot): pools hold $2,000 of total value at each tested spot.
• LMSR: b = 500, chosen so marginal depth at $0.50 matches the CPMM’s (p(1−p)/b = 2p/y). Capital asymmetry worth noting: LMSR’s worst-case operator loss is b·ln 2 ≈ $347, while the pools lock the full $2,000.
• Buys of $10–$250 USDC of YES at spots $0.50 / $0.90 / $0.95 / $0.99 — the tails are where prediction markets spend most of their life as resolution nears.

Results

Spot	Order (USDC)	CPMM exec	StableSwap exec	LMSR exec	LMSR new spot
$0.50	$10	$0.5050	$0.5002	$0.5050	$0.5099
$0.50	$50	$0.5250	$0.5012	$0.5238	$0.5476
$0.50	$100	$0.5500	$0.5024	$0.5456	$0.5906
$0.50	$250	$0.6250	$0.5063	$0.6011	$0.6967
$0.90	$10	$0.9090	$0.9004	$0.9010	$0.9020
$0.90	$50	$0.9450	$0.9021	$0.9048	$0.9095
$0.90	$100	$0.9900	$0.9043	$0.9093	$0.9181
$0.90	$250	$1.1250 ⚠️>$1	$0.9113	$0.9212	$0.9393
$0.95	$10	$0.9595	$0.9505	$0.9505	$0.9510
$0.95	$50	$0.9975	$0.9523	$0.9524	$0.9548
$0.95	$100	$1.0450 ⚠️>$1	$0.9546	$0.9547	$0.9591
$0.95	$250	$1.1875 ⚠️>$1	$0.9620	$0.9606	$0.9697
$0.99	$10	$0.9999	$0.9905	$0.9901	$0.9902
$0.99	$50	$1.0395 ⚠️>$1	$0.9924	$0.9905	$0.9910
$0.99	$100	$1.0890 ⚠️>$1	$0.9948	$0.9909	$0.9918
$0.99	$250	$1.2375 ⚠️>$1	$1.0025 ⚠️>$1	$0.9921	$0.9939

What the numbers say

1. CPMM fails at the tails, hard. At spot $0.99 a $50 buy already executes above $1.00 — a token that can never pay more than $1.00. Every ⚠️ cell is a guaranteed-loss trade the curve happily quotes. This confirms the feature doc’s structural-mismatch argument (x·y=k prices 0→∞; outcome tokens are bounded 0–1) with concrete sizes.
2. StableSwap has flat slippage but two disqualifying traits. (a) It still crosses $1 ($0.99/$250 → $1.0025) — flatness delays the bound violation, it doesn’t remove it. (b) The flatness is the second problem: at spot $0.50 a $250 buy moves execution only to $0.5063 — the curve resists repricing. StableSwap is built to defend a peg; a prediction market’s price is supposed to move with information. Amplification fights price discovery exactly when traders bring news.
3. LMSR respects the bound by construction and still reprices. Execution never reaches $1 (mathematically cannot), tail slippage is small ($0.99/$250 → $0.9921), and the “new spot” column shows real price movement at $0.50 (250 → 0.6967) — information moves the price, size doesn’t break the bound. It is also the classic prediction-market scoring rule, already named as the MM-agent evolution path in the design doc (§2.2.11 / §8), so choosing it converges two tracks instead of adding a second curve model.

Recommendation (for jay’s decision — dev item “(you) Curve decision”)

Option 2 — LMSR, with option 3’s tail guard kept anyway (max price-impact check in routing + slippage warning in the trade UI; cheap and curve-independent).

• Bounded 0–1 by construction; bounded operator loss (b·ln 2) instead of $2,000 locked per pool.
• Converges with the MM-agent evolution path instead of introducing a competing curve.
• On-chain prior art exists: Gnosis LMSRMarketMaker (audited, fixed-point exp/ln) — we integrate the pattern rather than inventing tail math. (Same clean-room stance as the CLOB: pattern, not code, unless the license allows import — check at implementation time.)
• Rejected: pure CPMM (quotes guaranteed-loss trades at the tails), StableSwap adaptation (still violates the bound at depth; amplification suppresses the price discovery a prediction market exists to provide).

Caveats: single-parameter sim (pool value $2,000, b=500, A=10); relative behavior is robust to these choices but absolute slippage numbers scale with liquidity. The LMSR/pool capital comparison is depth-matched at $0.50, which slightly flatters LMSR at the tails (its depth grows as p(1−p) shrinks it… i.e. thins there — yet it still beats CPMM in every tail cell).