Arctan AMM
2 min read
The pricing engine behind Raven — a bounded, self-balancing automated market maker built specifically for digital options.
The Problem
In any digital options protocol, if all traders bet on the same side, the protocol becomes insolvent — there isn't enough capital on the losing side to pay winners. Traditional solutions require centralized market makers, position caps, or outright trade rejection. None of these work for a decentralized, permissionless protocol.
The Solution — Arctan Pricing
Raven's AMM uses the arctangent function to price payout odds dynamically based on real-time imbalance between CALL and PUT volume in the pool. As one side gets crowded, that side's odds decrease and the opposing side's odds increase — automatically, algorithmically, with no human intervention.
P(x) = implied probability · x = signed CALL–PUT imbalance · α = sensitivity
The arctan function is naturally bounded between 0 and 1, making it directly interpretable as a probability. At equilibrium (equal CALL and PUT volume), P = 0.5, reflecting maximum uncertainty. CALL and PUT odds always sum to 1 for any given strike and expiry.
What This Means for Traders
- Always solvent — payouts are always fully backed by capital in the pool.
- Always transparent — current odds are visible on-chain before you commit any capital.
- Fully decentralized — no centralized market maker or admin required.
- Self-balancing — crowded sides get priced less favorably, naturally incentivizing contrarian positions.
The α Sensitivity Parameter
α controls how aggressively odds shift in response to pool imbalance. Higher α means premiums move more sharply as one side gets crowded; lower α produces more stable pricing. α is set per market by the protocol and may evolve as liquidity matures.