Option Premium

Intrinsic value is the payoff the holder would receive from immediate exercise, floored at zero. For a call it is the underlying price minus the exercise price when that difference is positive, otherwise zero; for a put it is the exercise price minus the underlying price under the same floor. Because exercise is a right and not an obligation, intrinsic value can never be negative.

Time value is the residual: the quoted premium less intrinsic value. It compensates the writer for the possibility that the underlying moves favourably before expiration. Time value is greatest when the option is near the money, where uncertainty about final moneyness is highest, and it shrinks as the option moves deep in or deep out of the money. At expiration time value is necessarily zero and the premium collapses to intrinsic value alone.

Six inputs drive the price of a European option. A higher underlying price raises call premiums and lowers put premiums; a higher exercise price does the reverse. Greater volatility of the underlying raises both call and put premiums, because the option truncates downside while leaving upside open, so dispersion is unambiguously valuable to the holder. A longer time to expiration normally raises premiums for the same reason, though for European puts a very long horizon can work against the holder because the maximum payoff is capped by the exercise price and receipt of it is deferred.

A higher risk-free rate raises call premiums and lowers put premiums, since the call holder effectively defers payment of the exercise price. Cash flows on the underlying, such as dividends or coupons, lower call premiums and raise put premiums because they reduce the price of the underlying without accruing to the option holder.

Listed options are quoted per unit of the underlying and settled against a contract multiplier, so an equity option quoted at a given premium is normally paid a hundred times over per contract. The buyer pays cash at initiation and has no further obligation; the writer receives cash, posts margin, and carries open-ended exposure. This asymmetry explains why implied volatility, extracted by inverting a pricing model against the observed premium, is treated as the market's forward-looking risk gauge rather than as a historical statistic.

Premiums also anchor cost comparisons across hedging structures. A protective put costs an explicit premium, while a collar finances part of it by writing a call. Under IFRS and US GAAP, purchased options are recognised as derivative assets at fair value, with the initial premium serving as the starting carrying amount.

Candidates should be able to compute intrinsic value from any spot and exercise pair, identify moneyness, and back out time value by subtraction. Know the no-arbitrage limits: a European call is worth at most the underlying price and at least the underlying price less the present value of the exercise price, floored at zero; a European put is worth at most the present value of the exercise price and at least that present value less the underlying price, again floored at zero. American options are worth no less than their European counterparts.

Put-call parity links the two premiums: a call plus a risk-free bond maturing at the exercise price equals a put plus the underlying. Rearranging it prices one option from the other, or constructs a synthetic position. Finally, express breakeven correctly: a long call breaks even at the exercise price plus the premium, a long put at the exercise price less the premium, with the opposite reading for the writer.