Uniform AMM Design for Prediction Market Outcome Tokens

Summary

The document develops pm-AMM, an automated market maker designed for binary prediction market tokens. It models token prices with Gaussian score dynamics: the event price tracks the probability that an underlying random walk finishes above a threshold. Because token volatility depends on both the current probability and time to expiry, conventional liquidity curves can expose providers to uneven losses as conditions change.

Using loss-vs-rebalancing (LVR) as its design objective, the authors derive a static invariant intended to make expected arbitrage loss proportional to pool value across prices under the model. A dynamic version scales liquidity down as expiry approaches, aiming to keep the expected loss rate constant over time. The paper compares its liquidity profile conceptually with constant-product and logarithmic scoring-rule designs. Its conclusions rely on prices equaling event probabilities and on predictable information arrival; markets driven by sudden shocks or strong risk and time preferences may not fit the model. The document presents theory and illustrations, not broad live-market performance evidence.

Key ideas

• Gaussian score dynamics model outcome prices as probabilities tied to a random walk's terminal value.
• The static pm-AMM is designed to make expected LVR uniform across prices under that model.
• The dynamic version reduces liquidity over time to target a constant expected loss rate.
• The approach assumes token prices equal event probabilities and information arrives predictably.
• Markets with abrupt information shocks may not suit the model.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.