Premium

The premium is the maximum loss for the buyer and the maximum gain for the seller. Sellers (“writers”) collect it in exchange for the obligation side of the contract — limited reward, potentially large loss.

The exam tests the direction each driver pushes value, not computation. The reliable trap is interest rates: a higher risk-free rate raises calls but lowers puts — students who memorized “higher rates raise premiums” miss the put. A higher dividend or yield on the underlying is the mirror image: it lowers calls and raises puts (only the call “likes” higher rates, since deferring the strike payment is worth more when money earns more). Don’t confuse premium with the strike (a fixed contractual term) or with intrinsic value alone: a deep out-of-the-money option has zero intrinsic value yet a positive premium from time value, so for American options the premium never falls below intrinsic value. Finally, a premium is paid upfront at initiation — unlike a forward or futures, which has zero value and costs nothing to enter.