Primitive has smart contracts which are a layer above a core Automated Market Maker (AMM) pool. The active AMM used by Primitive is SushiSwap, which uses the constant product curve.
The price of options on Primitive is therefore determined by the market, specifically by the ratio of assets in the AMM.
The short option tokens and underlying tokens are the assets in the pool, and the ratio between these assets is effectively the short option token premium.
Therefore, the long option token premium is 1 - shortOptionPremium.
That's a good question, using an AMM has explicit tradeoffs, including:
Enables liquidity providers to earn fees on option trading
Composability with other protocols
On-chain IV derivations from on-chain premiums
High slippage for large orders
These are trade-offs which will be improved on in the next version of the protocol, V2, which focuses on efficiency of liquidity and reducing slippage for traders.
This is a commonly asked question, and it's a clever mechanic the protocol uses in the background to get this to work:
Primitive Pool LP tokens are an instrument themself, and they will be utilized by other traders or liquidity providers for desired exposure. These pools also enable the LPs to get exposure to option trading fees, which is an avenue for yield that isn't widely available in DeFi.