Option Pricing Example

Suppose Alice wants to purchase a 1 SOL Call Option with a strike price of $25, set to expire in one month, from the Automated Market Maker (AMM). Currently, SOL is trading at $20, which indicates a 25% increase above the spot price. Over the past three days, the historical volatility has been 80%, with a Skew Ratio of 1.25, leading to an Implied Volatility (IV) estimate of 100%. Using the IV estimate and other known inputs, the Black-Scholes (BS) model calculates a Mark Price of 0.04 SOL per contract.

Once the Mark Price is determined, the bid-ask fee takes into consideration the delta impact of the transaction on the AMM. In this case, the trade reduces the AMM's delta risk, resulting in an ask multiplier of 1.1. This multiplier is combined with the Mark Price to establish an ask price of 0.04 * 1.1 = 0.044 SOL per contract.

Alice considers 0.044 SOL to be a fair price and decides to move forward with the purchase. Since 1 SOL collateral is secured until the option contract expires, the net change in SOL collateral usage is 1 - 0.044 = 0.956 SOL. With an interest rate of 3% APR, Alice must also pay a capital utilization fee of 0.956 x 1/12 x .03 = 0.00239 SOL.

Finally, a standard trade fee of min(10% of the trade price, 0.3% of the underlying) = 0.003 SOL is paid to the protocol.