Call Options Explained: The Long Call, Payoff and Greeks

The narration of the video, as text.

0:00The question

Pay a fraction of an index's value today to gain on every point it rises above a price fixed now, until a set date. What is that, really? A leveraged bet that the price will rise. But to win it, being right isn't enough.

0:17Welcome

Welcome to the LiveGexLevels options school. One idea at a time, from the first contracts in history to the strategies traders use today. This is education, not advice. You decide, and you trade with your own broker.

Second episode: the long call. The first options listed in Chicago, in 1973, were all calls. Puts arrived four years later. So that's where we start. We'll see what you buy, why the curve looks the way it does, how it changes with time, how you can get out before expiry, and the three numbers that move it: delta, theta and vega.

1:07What you buy

A call is the right to buy the underlying at a fixed price, the strike, by a date, the expiry. You pay for that right today: the premium. An index can't be bought as such, so on an index the call is settled in cash: at expiry you receive the difference between the index and the strike, if the index ends above the strike. A concrete case: the S&P 500 future, ES. To hold one contract overnight, your broker blocks about 28,000 dollars of buying power, and if the index falls, you can lose far more than that. Now take a call on the index, with example numbers: strike 7,800, where the index is, and a month to go. It costs 148 points, about 14,800 dollars, and at first it moves much like that future. Similar exposure, about half the capital, and the most you can lose is what you paid. But it doesn't come for free: the call has a deadline, and if the index stands still until expiry, it's worth zero. So let's see how it works.

2:15At expiry: the hockey stick

Let's start from the end: the day it expires. If the index closes below 7,800, the right is worth nothing, and you've lost the premium. Only the premium, never more, even if the index opens with a big gap down. A stop on the future can't promise that: a gap can jump right over it. Above 7,800, every point the index gains is a point for you. You break even at 7,948, the strike plus the premium. That's the shape at expiry: flat, then a straight line up. Traders call it the hockey stick.

2:54Before expiry: a softer curve

But before expiry, the picture is different. Look at the two curves. The dashed one is the stick: the result at expiry. The solid one is the result if you sold the call today. Right after you buy it, it crosses zero at 7,800: sell it back at once and you get about what you paid, leaving aside, for now, the spread between the buying and the selling price. So why isn't the curve a hockey stick from day one? Because the contract still has time ahead of it, and time is worth something. Think of a real case. You pay 5,000 euros today for the right to buy a flat at 300,000 within a year. If a month later flats like it sell for 330,000, your right is worth at least 30,000: anyone would buy it from you. If they drop to 280,000, your right is worth less, but at worst, at the end of the year, you simply don't buy: you lose the 5,000, no more. And if prices are still at 300,000, your right is still worth something: there are eleven months left for them to rise. With one week left, it's worth almost nothing. It's like an insurance policy: with a year of cover left it's still worth a lot; the day before it ends, almost nothing. A call works the same way. Its price has two parts. The intrinsic value: what it would pay if it expired right now, the index minus the strike, or zero. And the time value: the rest, what you pay for the time left. Today, at 7,800, the intrinsic value is zero: all 148 points are time value. If the index rises, the call you bought when the index was lower is worth more: at 7,900, about 208 points. If it falls, it's worth less: at 7,700, about 100. But however far the index falls, the call can't be worth less than zero: you never lose more than the 148 you paid. That's why the curve is softer: the time value lifts it above the stick, on both sides of the strike. At 7,700, those 100 points are all time value: selling today you'd lose only 48, at expiry all 148. And the lift is greatest near the strike, where the index could still go either way. Now let time pass, with the index still at 7,800. After ten days, the call is worth 119. After twenty, 82. Two days before expiry, 35. Like the flat with one week left, there's little time for anything to happen: the time value melts, and the curve settles onto the stick.

5:40You can get out before

And you don't have to wait for expiry. You can sell the call at any time while the market is open, at the price buyers are paying. On contracts that trade little, that price can sit well below the curve. American or European: the only difference is which days you can exercise it. An American option can be exercised on any trading day. A European one, like SPX options, only at expiry. Selling it works the same for both. And here's a detail: exercising early usually gives up the time value. Say the index is at 7,900 with ten days left, and the call is American. Exercise it, and you get the 100 points above the strike. Sell it, and you get about 145.

6:31Delta and gamma

Now the three numbers. The first is delta: how much the call moves when the index moves one point. It's the slope of the curve. On the chart, delta has its own line: the thin dash-dot one, read on the scale at the right. Far below the strike it's close to zero, far above it's close to one, and at the strike it's a little over one half: here, 0.54. But the slope itself changes as the index moves. That change has a name: gamma. As the index rises, the curve gets steeper, and the call gains more and more. As it falls, the curve flattens, and the call loses less and less. With 100 points either way, the call gains 60 but loses only 48. That imbalance in your favor is called convexity. And time sharpens it. Near expiry, delta turns almost into a step: zero below the strike, one above. On an option that expires the same day, a 0DTE, with six hours to go, gamma is 11 times higher than at 30 days, and it keeps climbing. That's what draws scalpers to it: a few points are enough to change the delta a lot. The price, as we'll see now, is time.

7:49Theta: the cost of time

The second number is theta: what one day costs. For our call, 2.7 points a day, almost 2% of its value. And it speeds up: with two days left, 9 a day, and on the last day, time takes all that's left. It bites hardest near the strike, exactly where the time value is. That's how you can be right about the direction and still lose. Take a call on our index that expires the same day, bought six hours before the close, for 12.3. Four hours later the index is up 5 points, and the call is worth 9.9. The move came, but too slowly.

8:32Vega: volatility

The third is vega: how much the call gains when implied volatility, the movement the market expects, rises one point. Here it's 15%: at 16, the call gains almost 9 points. Back to the flat: you bought the right to buy it at 300,000 when the neighborhood was quiet, and it cost little. Then a big project comes to the area, still uncertain: a metro station, or an incinerator. Prices could rise a lot, or fall a lot, and nobody knows which way yet. Your right is now worth more: the same right, bought today, would cost more than you paid. Prices haven't moved, and you already hold more value. It's the same imbalance as before: a wider range of possible prices means bigger gains above the strike, while below it you still lose only the premium. On the index, volatility tends to rise before big events, like a central bank decision. Ten days after buying, with the index still at 7,800, our call is worth 119: time has taken 29 points. But if volatility has risen from 15 to about 20% in the meantime, it's worth about 157: more than the 148 you paid, with the index standing still. Vega shrinks with time too: two days before expiry, it's just over 2. And on an index there's a catch. Volatility usually falls when the price rises, and rises when the price falls. For a long call it works like a brake: on the way up it gains a little less, and on the way down it loses a little less. With the put, as we'll see, it's the opposite: volatility amplifies. Time and volatility both work against anyone who buys a call for a slow rise.

10:24Scalping and LEAPS

So who buys calls, and how? Two very different ways. Scalpers buy short-dated calls for quick moves: the convexity works for them, and the price they pay is theta, by the hour. At the other end, there are LEAPS. The Chicago options exchange created them in 1990: options that last a year or more, up to three at launch. A one-year call on our index costs 648 points and moves like about two thirds of an index. Since theta speeds up only near expiry, it loses just 1.1 points a day: for its price, a tenth of the 30-day call. The catch is vega: one point less of volatility costs it as much as 25 days of time, even with the index standing still. And more is at stake: 648 points, all lost if in a year the index isn't above the strike.

11:23In brief

In brief. A call is a leveraged bet on the rise, with a deadline, and the loss stops at the premium, even after a gap. At expiry it's a hockey stick: to remember it, the long call is the stick with the handle rising to the right. Before that, a softer curve: the stick plus the time value, which melts as time passes. You can sell it on any trading day, at the market price. Delta tells you how it moves, theta what each day costs, and vega what volatility does to its price. And being right isn't enough: the rise has to come, big enough, and in time. On the S&P 500, LiveGexLevels estimates during the session where the dealers' hedging piles up: useful levels to have in front of you when you plan where to get in and where to get out.

12:15Up next

Next episode: the long put, the protection we met with the farmer, this time on the index. We take requests, so tell us in the comments what you'd like us to explain. Before risking real money, practise with paper trading. And the guide is free with our newsletter, on livegexlevels.com.