The life of one option contract

Say you buy one AAPL $130 July 2015 call on . AAPL closes that day at $. The strike is $130, so the stock sits well below it: the call is out of the money. It has no intrinsic value yet. Every cent you pay is time value, the market's price for the chance that AAPL rises above $130 before July.

The reconstructed premium is $ a share. One contract covers 100 shares, so you pay $ today. That $ is the most you can lose on this trade, from this day on, whatever AAPL does. You pay it once, and no margin call is waiting for you: that is the buyer's side of an option, not the writer's.

Expiry is , the third Friday of the month, the standard expiry day for US equity options. That is calendar days away, about trading days. The contract is American style, so you could exercise it on any trading day between now and then, not only at expiry. That fact is what makes the decision two sections from now a real one.

On Monday 27 April 2015, Apple reports its fiscal second-quarter results after the market closes. Investors like what they see, helped by strong iPhone sales in China. AAPL had already climbed into the report; it closes at $ on the 27th, the highest close in this whole window. The next session, , the stock closes at $, already giving back some of the move.

For the first time, your $130 call is in the money. The stock sits $ above the strike, so intrinsic value is $. The reconstructed premium is $: intrinsic value $ plus time value $. The premium has risen from $ to $ in trading days, up . On paper, per contract, you are up $. You have sold nothing yet, so this gain is unrealised.

Because this is an American option, you have a real decision today, not just at expiry. Sell the call, exercise it, or hold it?

After the pop, AAPL drifts down through May and June. By 1 June it closes at $, just above the strike, so the call keeps a sliver of intrinsic value ($), but time value has already slipped to $. By 15 June the close is $, back below the strike, and the premium is down to $. Late in June the Greek debt crisis reaches a head: capital controls go on over the weekend of 27 to 28 June, and global markets, AAPL included, step down. AAPL closes at $ on 29 June.

Two forces now pull the option down at once. The stock is moving away from the strike, so intrinsic value stays at zero. And every day that passes eats a little more time value, whatever the stock does. That second force has a name, theta. I only name it here; Topic 14 covers it properly.

The low point of the whole window comes on : AAPL closes at $, and the reconstructed premium falls to .

AAPL claws back some ground into expiry: $ on 16 July, then $ at the close on Friday 17 July, expiry day. That is cents under the $130 strike. The call finishes out of the money. Its payoff is exactly zero.

Your profit on the trade is not the same thing as the payoff. Profit is payoff minus the premium you paid: 0 − = −$. You lose the whole $, and nothing more. That ceiling was fixed on the day you bought the option, back on ; it never moved, however far AAPL fell in between.

Now you know how the contract ended. Lay the three exits side by side and the lesson is not about predicting Apple. It is about what to do with an option once you turn out to be right.

Sell at the 27 April peak: +$ per contract. Exercise at the same peak: −$ per contract. Hold to the 17 July expiry: −$ per contract.

The stock did move in your favour, briefly. Being right about direction was not enough on its own. Exercising threw away time value the market was still paying for. Holding gave that time value back to the market for nothing, one day at a time, until none was left. Selling was the only exit that collected the full value the contract had reached, intrinsic value and time value together.

The standing rule survives the whole story unbroken: sell an option rather than exercise it, while time value is still positive. On 27 April 2015, that rule was worth $ per contract.

Every option has two sides. On , somebody wrote (sold) you this call and collected your $ premium. Their result is the mirror image of yours, because in money an option is a zero-sum contract between the two of you: whatever you gain, the writer loses, and whatever you lose, the writer gains.

If the writer had bought the contract back at the 27 April peak, they would have paid $ to close a position they sold for $, a loss of $, the exact mirror of your gain that day.

If the writer instead held the short position to 17 July, as this trade actually plays out, the call expires worthless and the writer keeps the full $: pure profit, the exact mirror of your loss.

But the shape of the risk was never symmetric. Your worst case, as the buyer, was fixed at $ the moment you paid it. The writer's worst case, in principle, has no ceiling: if AAPL had kept climbing past $ and beyond, the writer's loss would have grown with the stock, dollar for dollar (unless they held the shares as a covered call, which is Topic 14 again). This trade happened to end well for the writer. Many do not. That asymmetry is why buying options and writing them are such different businesses, even on the same contract, and it is where Lecture 9 leaves off.