The Right

An option is a right without a matching obligation. The holder may act; the seller must, if asked. Almost everything difficult about options follows from the problem of putting a price on that asymmetry across time and uncertainty.

The first group of terms describes the contract: what each side may do, what the price is made of, and where the strike sits. The second describes the pricing and risk apparatus, which is where the subject earns its reputation for difficulty.

Worth flagging early: the Greeks are model outputs, not measurements. They inherit the assumptions of whatever model produced them, and they describe an instant rather than a range.