"A call option is a contract that gains value when the underlying stock rises. In the most basic sense, then, a call option is a bet that the underlying security will rise in price, enabling you to profit from your investment. However, call options can also be combined with other types of option contracts to construct a number of different bullish, bearish, and directionally neutral trading strategies." - https://www.schaeffersresearch.com/education/options-basics/getting-started-with-options/what-is-a-call-option
When call option tokens are held by a user, that user is effectively long on the option token, which will have its value fluctuate based on multiple variables: time to expiry, volatility, underlying price, change in underlying price, and interest rates. These variables are called the Greeks.
Options have a few parameters which need to be chosen: strike price, strike date, underlying asset, and quote asset. Call options on Primitive should have the quote asset as Dai, and the underlying asset as the desired underlying. But how are the other parameters chosen?
As a protocol, the goal is to have a sustainable methodology to choose these parameters. Both traders and liquidity providers will have different desires to enter a market based on the option parameters. Primitive uses snapshot (https://snapshot.page/#/primitive.eth) to propose option markets! Active liquidity providers who hold LP tokens are given voting power for these proposals. In the next upgrade of the protocol, it will be possible to aggregate option liquidity voting power so all liquidity of a single provider is taken into account, enabling them to vote on the option markets they want to be in.
The simple explanation is that Primitive options can be traded in any AMM. Short option tokens and underlying tokens in the AMM pools act as "open interest", and the exchange ratio between them is used to calculate the premium. For example, if 0.8 ETH can be swapped to 1 short option (short options are scaled by the strike price), the exchange ratio is 0.8. Therefore, the cost to buy a long option token is 1 - 0.8 = 0.2 ETH. To summarize, the option premiums are determined by the market, and not algorithmically.
$CallExchangeRatio = Short Options/StrikePrice * 1 / UnderlyingTokens$
$Premium = 1 - ExchangeRatio$
Primitive options have two pieces: the long and short option tokens. The long is the actual option, while the short option is the counter-party. Using the protocol's bridge contracts (called Venues), the protocol enables these options to be traded on any AMM. The first bridge contract is for Uniswap/SushiSwap, and it solves a few issues by taking a unique approach. Short option tokens are provided as liquidity along with underlying tokens. Short option tokens in this pool act as open-interest, allowing anyone to borrow the short option to close their long positions (effectively, selling their long options). While underlying tokens in this pool also act as open-interest, allowing anyone to borrow the underlying tokens to mint new options (both long and short). The newly minted short options get sold back to the pool, and the difference between the borrowed underlying and proceeds from selling the short options is the premium. For example, if a user borrows 1 ETH, mints 1 long option + 200 short options, and then sells the 200 short options for 0.8 ETH, the premium is (1-0.8 = 0.2 ETH). There is no algorithm or closed-form solution that accurately prices American options, especially over longer periods. Longer dated options are particularly attractive because they cost significantly less upfront when compared to the notional value they control. These options are priced better by the market than any formula, which makes them cheaper.