# Greek Graphs Tell the Story of Call Strategies

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Call options are complicated because there are a lot of moving parts. If you’re new to options, you may not realize that there’s more to them than just anticipating how much price will move. You also have to forecast when price will move and how market makers and other option traders will react to changes in the underlying’s price. Of course, these changes affect a call seller differently than a call buyer. The options greeks help option traders estimate how an option will change value based on changes that take place over the life of the option. However, this not only changes an option's value due to the underlying having a price move, it also happens as a result of the march of time, and other changes. So, if traders can visualize the changes in the greeks, it’ll help them build expectations for how the option itself moves. In this article we’ll explore how. But before we get into the greeks, let’s review the basic structure of an options premium.

An options premium consists of intrinsic and extrinsic value. Intrinsic value of in the money options is the value an option has only because of where the underlying stock is right now, at expiration, an option's value is zero. Intrinsic value is calculated by taking the difference between the strike price and the current price of the underlying. For a call option, if the underlying’s price is above the strike price, the intrinsic value will be the difference between the two prices. If the underlying’s price is below the stock price, then the option will not have intrinsic value. You may remember that options with intrinsic value are in the money and options without intrinsic value are out of the money.

Extrinsic value is the difference between the call premium and the intrinsic value. Extrinsic value is made up of time value and implied volatility. We’ll discuss these two parts in further detail as we talk about the greeks. Notice in Figure 1 how the extrinsic values are highest near the at-the-money option. As we explore the greeks, you’ll learn why.

FIGURE 1: EXTRINSIC VALUE IS THE HIGHEST WHEN THE OPTION IS AT THE MONEY.

The greeks help traders understand why an options premium changes. Image source: the paperMoney® platform. The example used is for illustrative purposes only. Not a recommendation of any security or strategy. Past performance does not guarantee future results.

There are four major greeks: delta, gamma, theta, and vega. Delta and gamma deal mostly with the price of the underlying security, whereas theta and vega deal with the extrinsic value. Let’s discuss each, starting with delta.

# Delta

Delta measures how much the options premium changes with a \$1 move in the underlying price. For example, if a call option has a delta of .53 and the underlying climbs \$1, the option will increase \$0.53 in value. Notice the purple line in Figure 2. This is a graph of the change in delta for a call option. The purple line includes both intrinsic and extrinsic values. The green line includes only intrinsic value.

FIGURE 2: BEFORE EXPIRATION, THE DELTA FOR A CALL OPTION RISES AS THE UNDERLYING’S PRICE INCREASES.

A delta of 1 on the y-axis is equal to 1,000. Image source: the paperMoney platform®. The example used is for illustrative purposes only. Not a recommendation of any security or strategy. Past performance does not guarantee future results.

Let’s discuss the changes in the purple line. If the underlying moves from \$55 to \$56, the delta will hardly increase compared to a change from \$63 to \$64. So, if you’re a call buyer, you might consider options that are closer to being at the money because you can capitalize on bigger moves. Of course, those big moves cut both ways, so beware. If you’re a covered call seller who wants to avoid losing stock through assignment, consider selling out of the money calls so underlying price movements have little effect on your trade.

# Gamma

Gamma measures how much delta will change with each \$1 move in the underlying. Let’s look back at Figure 2. Previously, we observed that the ends of the purple curve climbed at a slower rate. The middle of the curve is steeper, which reflects a higher rate of change. The rate of change is what gamma measures. Now, look at Figure 3. Notice the purple line swells in the middle and is flatter on the ends. This reflects changes in the delta curve.

FIGURE 3: GAMMA ACCELERATES AS THE UNDERLYING’S PRICE RALLIES INTO THE STRIKE PRICE AND DECELERATES AS IT RALLIES PAST THE STRIKE PRICE.

Delta can only rise to a value of 1, so delta will grow at a faster rate when the option is at the money or nearly at the money. Image source: the paperMoney® platform. The example used is for illustrative purposes only. Not a recommendation of any security or strategy. Past performance does not guarantee future results.

These two curves provide insight as to why extrinsic value is the highest when the option is at the money. When an option is at the money, it has the highest risk to the seller. Often the seller is a market maker. Higher extrinsic value absorbs some of the price movement. The green gamma line shows how sensitive delta is when extrinsic value is a non-factor. So, as extrinsic value is reduced, gamma becomes a bigger factor.

# Theta

Theta is our first greek dealing directly with extrinsic value. It measures how sensitive an option is to time decay. Remember, time decay works against option buyers and favors option sellers. Figure 4 shows theta is highest for at-the-money options and lower for out-of-the-money and deep in-the-money options.

FIGURE 4: THETA IS THE HIGHEST WHEN AN OPTION IS AT THE MONEY.

Theta accelerates as the underlying’s price rallies into the strike price and decelerates as it rallies past the strike price. Image source: the paperMoney® platform. The example used is for illustrative purposes only. Not a recommendation of any security or strategy. Past performance does not guarantee future results.

Earlier we observed that the biggest changes in delta and gamma, and, by extension, the options premium, occur when the option is at the money. For option buyers, the deck is kind of stacked against them because they have to overcome the extrinsic value that is working against them, in other words, time decay.

Option sellers can get the most extrinsic value by selling at-the-money options. However, they have a higher likelihood of assignment by doing this. So, they need to reconcile this risk by either accepting assignment or reducing the likelihood of assignment by selling out of the money for a smaller premium.

# Vega

Vega measures how sensitive an option is to changes in implied volatility. Figure 5 shows that when the option is at the money, it has the highest sensitivity to implied volatility. Implied volatility can rise and fall independent of price movement; however, it commonly rises when price falls. This means the curve below can shrink and grow. Notice how the green line is flatlined on the bottom of the chart. This shows us that at expiration there’s no implied volatility.

FIGURE 5: THE VEGA CURVE CAN SHRINK OR EXPAND DEPENDING ON CHANGES IN IMPLIED VOLATILITY.

Vega is highest at the money but shrinks as price pulls away in either direction. Image source: the paperMoney® platform. The example used is for illustrative purposes only. Not a recommendation of any security or strategy. Past performance does not guarantee future results.

So, what does this tell us about call strategies? Well, option buyers would prefer to buy when implied volatility is low, and it’s a bonus if implied volatility rises. In fact, if a trader bought an out-of-the-money option, she would benefit from both the rising price and the rising implied volatility if the stock moved in her favor. However, that’s the trick. Buying out-of-the-money options is a strategy with a low probability of success.

An option seller who sells at the money will benefit if the implied volatility drops, but will hurt the most if the implied volatility rises. Therefore, a seller may benefit most by selling when implied volatility is high and then falls.

# Conclusion

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Delta is a measure of an option's sensitivity to changes in the price of the underlying asset.
Gamma is a measure of delta's sensitivity to changes in the price of the underlying asset.
Vega is a measure of an option's sensitivity to changes in the volatility of the underlying asset.
Theta is a measure of an option's sensitivity to time decay.