What an option actually is

An option is a right, not an obligation, to trade something at a fixed price before a fixed date. That is the whole definition. Everything else — the Greeks, the smile, the strategies — is bookkeeping on top of it.

Calls and puts

A call gives you the right to buy at the strike. You want the price up. A put gives you the right to sell at the strike. You want the price down.

Whoever sold you that right has the mirror position and an obligation rather than a choice. This asymmetry is the entire product: the buyer's loss is capped at the premium, and the seller's is not.

Move the spot slider on that chart. Below the strike the line is flat — you simply do not exercise, and the premium is gone. Above it the payoff turns and climbs at the same rate as the underlying. The kink sits exactly on the strike, which is why option payoffs are drawn with corners rather than curves.

Strike, expiry, premium

Three numbers define a contract.

• Strike — the price you may transact at.
• Expiry — the date the right lapses.
• Premium — what the right costs.

A contract usually covers 100 shares, so a premium quoted at 3.02 costs £302. The calculator calls this the multiplier, and forgetting it is the most common arithmetic error in option trading.

Moneyness

An option is in the money if exercising it right now would be worth something, at the money if the strike is roughly spot, and out of the money if exercising would be pointless. A call at a 90 strike with spot at 100 is 10 in the money; the same call with spot at 80 is 10 out of the money and worth only whatever chance remains.

Intrinsic and extrinsic value

Premium splits cleanly into two parts.

Intrinsic value is what the option is worth if it expired this second — max(spot − strike, 0) for a call. It cannot be negative, because you would simply not exercise.

Extrinsic value is everything else: the price of the time remaining and the uncertainty in it. It is the entire premium of an out-of-the-money option, and it decays to nothing by expiry with mathematical certainty.

That decay is the central fact of being long options. You are paying, every day, for the possibility that you are right. Set the days-elapsed slider on the chart above and watch the pre-expiry line sag towards the hard expiry line — that gap is extrinsic value draining away.

Why the expiry line has corners

Look at the two lines on the chart. The solid one is the payoff at expiry: piecewise linear, kinked exactly at the strike, because at expiry an option is worth its intrinsic value and nothing else.

The dashed one is the modelled value before expiry, and it is smooth. It sits above the expiry line everywhere, and the distance between them is the extrinsic value you still own. Both lines meet at expiry. Every options strategy is, in some sense, a bet about how those two lines converge.

What comes next

The Greeks are the four sensitivities that describe how the dashed line moves when something changes — spot, time, or volatility. They are less intimidating than the notation suggests, and they are the subject of the next page.