1. Call and put: one party's right is the other's obligation

Derivatives 2: Options, the mechanics

The previous level ended with a perfectly symmetrical contract. In a future, two parties commit today to exchange something on a given date at an agreed price, and both are equally bound. An option breaks that symmetry down the middle, and in that break lies everything that makes this family of instruments different.

A right for one, an obligation for the other

An option is a contract in which one party buys the right — not the obligation — to buy or sell an asset at a price fixed in advance, within a given period. The other party sells that right and is obliged to deliver if the first decides to exercise it.

There are two types, and it is worth pinning them down from the first minute because everything else is built on top of them:

• Call (option to buy). It gives its buyer the right to buy the asset at the agreed price. Whoever sells it is obliged to deliver at that price if called upon.
• Put (option to sell). It gives its buyer the right to sell the asset at the agreed price. Whoever sells it is obliged to buy at that price if it is imposed on them.

In every contract there is always a buyer who has a decision to make and a seller who has none: he simply waits. That wait is not free, and that is why he is paid up front.

The five pieces that define any contract

An option is not fully described until these five things are settled:

• The underlying. The asset everything depends on: a share, an index, a commodity, a currency.
• The strike price (or *exercise price*). The price at which the buyer will be able to buy, if it is a call, or sell, if it is a put. It is fixed from the moment of signing and does not move.
• The expiry. The date on which the right lapses. Past that date, an unexercised option is worth exactly zero: it is not that its price falls, it is that it ceases to exist.
• The premium. The price of the contract. The buyer pays it and the seller collects it on the spot, and it is never refunded, whether it is exercised or not.
• The multiplier. How many units of the underlying one contract covers.

The multiplier: why a premium of 3 costs 300 euros

This detail throws people more than any other. Premiums are quoted per unit of underlying, but they are traded in contracts, and a standard contract on shares covers 100 of them.

Let us work with an example we shall keep for the whole level. A share trades at 100 euros. There is a call with a strike of 105 and expiry three months away, whose premium is quoted at 3.

Buying one contract of that call does not cost 3 euros: it costs 3 times 100 shares, that is, 300 euros, and gives the right to buy 100 shares at 105 each, an outlay of 10,500 euros if you exercise. Somebody who believes he is risking "three euros" has committed 300 and has opened the door to a trade of 10,500. From here on we shall reason per unit, but do not lose sight of the factor of 100.

The fundamental asymmetry, with the numbers in front of you

Here is the heart of the matter. The buyer pays 3 and knows with absolute certainty what his worst case is: losing those 3. If the share collapses to 40, he does not exercise and his loss is 3. Not a cent more. The buyer's loss is limited to the premium.

His profit, by contrast, has no defined ceiling. If the share rises to 130, he exercises: he buys at 105 something worth 130 and, after the premium, takes home 22. If it rises to 200, he takes home 92.

The seller lives the exact mirror image. He collects 3 on day one and that is all he can ever make, whatever happens: if the share collapses he keeps 3, and if it sits still he also keeps 3. His potential loss is the flip side of the buyer's gain: at 130 he loses 22, at 200 he loses 92.

From this comes the break-even point, the price at which the buyer neither gains nor loses: you have to recover the strike and the premium on top, that is 105 plus 3, 108. Below it he loses something; above it, he gains.

That asymmetry is not a gift: it is paid for with the premium, which is dearer the more time is left and the more turbulence is expected in the underlying. How that turbulence is measured is the subject of the next level.

European style and American style

The names are historical and have nothing to do with geography: both styles are traded everywhere today.

• A European-style option can only be exercised on the expiry date.
• An American-style option can be exercised on any business day up to expiry, at the buyer's choice.

American flexibility can never be worth less than European, because it includes everything the latter allows and something more. In practice, as we shall see in the third module, that "something more" is worth far less than intuition suggests. As a rough guide: options on individual shares tend to be American, and many on indices are settled European-style and in cash.

Worked case: three outcomes for the same contract

You buy the 105 call for a premium of 3, with the share at 100. Three months later:

• The share closes at 99. The right to buy at 105 is useless: it is cheaper in the market. You do not exercise. Loss: 3.
• The share closes at 106. You exercise, because buying at 105 something worth 106 recovers 1. Net result: a loss of 2. It is exercised and money is still lost, because the premium is already paid.
• The share closes at 118. You exercise, you gain 13 of difference and, once the premium is subtracted, you are left with 10 a unit. With the multiplier, 1,000 euros on an initial investment of 300.

This material is education about how an instrument works, not a recommendation to trade it.