Lyra is an automated market maker (AMM) designed for trading European options on the Ethereum blockchain. It utilizes strike-adjusted implied volatilities (IV) based on a Black Scholes model to determine option prices. Additionally, Lyra takes into account Vega and Delta risks that liquidity providers (LPs) are exposed to.

Lyra accepts stablecoins as collateral and offers options in rounds. Each round lasts for 28 days and includes 4 discrete expiry dates (7, 14, 21, and 28 days from the start of the round). The liquidity is divided into two sub-pools: the Collateral Pool, which collateralizes options and handles premium payments, and the Delta Pool, which hedges the AMM's delta exposure by trading the underlying asset.

The primary objective of an options market maker is to find an IV value that balances the demand and supply of options. When this equilibrium is achieved, the AMM can generate fees from trades without assuming significant risk since it buys and sells options in equal quantities. Lyra's AMM is designed to efficiently respond to changes in supply and demand to maintain this IV level. The market-derived IV value is then used to calculate the Black Scholes price of an option (W).

Liquidity providers can deposit sUSD into a Lyra market maker vault (MMV) to earn trading fees from protocol users. Users have the flexibility to deposit or withdraw funds from the AMM at any time, subject to a short delay. Once the 7-day cooldown period ends and circuit breakers are cleared, the net asset value (NAV) of the pool, which includes free liquidity, the delta hedging position, and the pool's option exposure, is calculated using a geometric time-weighted average value (GWAV). The value of each LP token is determined by dividing the NAV by the total number of LP tokens in circulation. LP tokens are minted or burned based on the value of the deposited or withdrawn capital divided by the value of a single LP token.