Expiring Assets in Automated Market Makers
Kenan Wood, Maurice Herlihy, Hammurabi Mendes, Jonad Pulaj
TL;DR
The paper tackles the challenge of trading expiring assets in automated market makers by introducing a hybrid DEX that fuses an LP-controlled state-curve AMM with last-minute buyer and producer order books and a two-stage market clearing mechanism. It develops a formal framework where LPs influence prices through c via a geometric-mean aggregation, and introduces liquidity freezing to manage risk as expiration nears, while ensuring liveness and market clearance through auctions near t_r. Key contributions include the state curve construction f_{c,x0,y0}, the unique aggregation c = ∏ c_l^{s_l}, the freezing/removal/liquidation mechanisms, and a rigorous proof of liveness and market clearance. The design enables robust, live trading of expiring tokens on-chain and provides explicit incentives and protections for liquidity providers, with practical applicability to real-world expiring assets.
Abstract
An automated market maker (AMM) is a state machine that manages pools of assets, allowing parties to buy and sell those assets according to a fixed mathematical formula. AMMs are typically implemented as smart contracts on blockchains, and its prices are kept in line with the overall market price by arbitrage: if the AMM undervalues an asset with respect to the market, an "arbitrageur" can make a risk-free profit by buying just enough of that asset to bring the AMM's price back in line with the market. AMMs, however, are not designed for assets that expire: that is, assets that cannot be produced or resold after a specified date. As assets approach expiration, arbitrage may not be able to reconcile supply and demand, and the liquidity providers that funded the AMM may have excessive exposure to risk due to rapid price variations. This paper formally describes the design of a decentralized exchange (DEX) for assets that expire, combining aspects of AMMs and limit-order books. We ensure liveness and market clearance, providing mechanisms for liquidity providers to control their exposure to risk and adjust prices dynamically in response to situations where arbitrage may fail.