3. What a premium breaks down into: intrinsic value and time value

Derivatives 2: Options, the mechanics

So far the premium has been a figure dropped out of the sky: 3 for the 105 call, 2 for the 95 put. It is time to open it up. Every premium breaks down into two parts of very different natures, and separating them lets you stop seeing an option's price as an opaque number.

Intrinsic value: what it would be worth if it expired right now

Intrinsic value is what the buyer would collect if the contract expired right now. It is worked out without any mystery:

• In a call, it is the underlying's price minus the strike price, and if that comes out negative, it is zero.
• In a put, it is the strike price minus the underlying's price, and if that comes out negative, it is zero.

The zero clause captures the fact that the buyer is never obliged to exercise: a 105 call with the share at 90 is not worth minus 15, it is worth zero, because nobody exercises a right that harms them.

With the share at 100, the 105 call and the 95 put both have zero intrinsic value. And yet the first trades at 3 and the second at 2. That surplus is the other piece.

In, at and out of the money

Comparing the underlying's price with the strike price gives three labels that are used constantly:

• In the money. It has positive intrinsic value: the 105 call if the share trades above 105, the 95 put if it trades below 95.
• At the money. The underlying is at the strike price or very close to it. Intrinsic value zero or nearly so.
• Out of the money. There is no intrinsic value at all. With the share at 100, the 105 call and the 95 put are both out.

A word of warning: being in the money does not mean the trade is making money. If the share rises to 107, the 105 call is in the money, but its buyer, who paid 3, is still losing. The labels describe the relationship with the strike, not with the premium.

Time value: what you pay for what may still happen

Time value is the remainder: premium minus intrinsic. It is what the buyer pays for the possibility that things improve before expiry, and what the seller is paid for putting up with it.

With the share at 100 and three months ahead, the 3 of the 105 call is pure time value. Nobody would pay 3 for a right worth nothing today were it not that in three months the share could be at 120.

Two things feed it. The time remaining: more time, more things can happen. And how much turbulence is expected in the underlying: a share that moves 1% a month and one that moves 15% cannot have the same premium even if they share price, strike and expiry. How that turbulence is priced is the business of the next level.

Why time value is greatest near the strike price

This is the part intuition does not hand you for free. Picture three calls on the same share, which trades at 105, with the same expiry and these indicative premiums:

• 140 call. Premium 0.20. Intrinsic 0, time 0.20. It is so far away that hardly anybody pays for it.
• 105 call. Premium 4. Intrinsic 0, time 4. Here the uncertainty is at its greatest: any movement decides the contract's fate.
• 70 call. Premium 35.40. Intrinsic 35, time 0.40. It is almost certain to end up exercised: the contract already behaves like the share itself.

The pattern is clear: time value is greatest when the underlying sits at the strike price and it fades as we move away in either direction. It pays for uncertainty about the outcome, and that uncertainty is greatest right on the border between exercising and not exercising.

There is a second law, and there is no appealing against it: when expiry arrives time value is exactly zero. There is nothing left to happen, and the option is worth not a cent more or less than its intrinsic value. That fading is not linear: it accelerates in the final weeks and is especially brutal in options that are at the money. The buyer suffers it and the seller collects it.

Why exercising early almost never pays

This is where the question of American style is settled. You are long the 105 call, the share rises to 130 and you want to take the profit. Two routes:

• Exercise. You buy at 105 and sell at 130. You collect 25, that is, the intrinsic value. Not a cent more.
• Sell the contract. If it has two months left, it will trade above 25 — say 27 — because it still carries time value. You collect 27.

Exercising early gives away the remaining time value. And there is a second reason: it forces you to pay out the 105 today instead of in two months' time, and that money could be earning something. That is why, on a share without dividends, exercising an American call before expiry is never the best decision: if you want out, you sell the contract.

Two honest qualifications. On puts deep in the money it can indeed pay to exercise early, because collecting the exercise proceeds sooner has value and the fall is capped by zero. And on calls on shares that pay dividends it can be worth exercising just before the ex-dividend date, since the option holder does not receive dividends. These are the exceptions documented in the classic derivatives literature.

Worked case: the same call, three moments

We stay with the 105 call, bought for 3 with the share at 100 and three months ahead:

• A month later, the share is at 104 and the call trades at 2.60. Intrinsic 0, time 2.60. The share has risen 4 euros and the option has lost value: the time consumed weighs more than the move toward the strike.
• Two months later, the share is at 112 and the call trades at 7.80. Intrinsic 7, time 0.80. The bulk of the premium is now intrinsic.
• At expiry, the share is at 112 and the call is worth exactly 7. The time value has disappeared completely.

The figures in this case are a coherent teaching illustration, not the quoted price of any particular contract.