The sensitivity of option prices to changes in time, volatility, and the price of the underlying are commonly referred to as “Greeks.” As you prepare for earnings season, here's an overview.

By Kevin Hincks
July 3, 2018

Photo by Getty Images

- An option's delta and gamma reflect its sensitivity to changes in the price of the underlying
- An option's theta measures how its price changes with the passage of time
- An option's vega reflects its sensitivity to changes in implied volatility

Seasons change, four times a year to be exact. As each year progresses, the smell of freshly cut grass fades into the crunch of freshly fallen leaves, and then the snow falls, and then...the cycle starts anew. No surprise there.

Also four times a year, companies report their quarterly earnings. But unlike spring, summer, fall and winter, earnings season can surprise. These earnings surprises can be positive or negative, and a stock’s reaction can be moderate or extreme. Have you considered options strategies this season?

Options aren’t suitable for everyone but they are often used by sophisticated investors looking for a way to use leverage to speculate on direction, as well as volatility, during earnings season. Options are also used to potentially help protect a portfolio against adverse moves in the portfolio itself or its components.

Do you find yourself in need of some options education, or perhaps a refresher? If so, we’d like to suggest a foreign language—Greeks—the unofficial language of options. Understanding options terminology can help you understand how options prices move, and how to assess potential risks on options positions, during earnings season, or any season.

There are three major variables that affect the price of an option: changes in the price of underlying, changes in implied volatility, and the passage of time. Interest rates and dividends also play a part, but generally to a lesser extent, in that changes occur less frequently. The sensitivity of options prices to changes in these variables are known collectively as “Greeks.”

An option's delta and gamma relate to changes in the price of underlying. Option theta measures the effects of time. Option vega (and yes, we know “vega” is not a letter in the Greek alphabet), deals with changes to implied volatility. And as you can imagine, vega is particularly important during earnings season. So let the lesson begin.

*But one caveat before we get started. These measurements are, in general, theoretical, based on an option pricing model such as the *Black-Scholes* model. There’s no guarantee that, in the real world, an option’s price will move in lockstep with the theoretical changes predicted by a model.*

An option’s price typically changes when then the price of the underlying changes. Delta says by how much. It’s defined as an option's sensitivity to changes in the price of the underlying. The option is going to move at some percentage (100% or less) of what the underlying does. So if an option has a 50 delta—which might be expressed as .50 because it’s a percentage—and the underlying moves by $1, then the option should move by 50 cents.

Call options have positive deltas since calls typically increase in value when the underlying moves higher. Puts, on the other hand, have negative deltas since put prices typically move in the opposite direction of the underlying. But don’t worry; you needn’t be an expert on the math behind the pricing formula to calculate any of this. If you’re a TD Ameritrade client, it’s all there for you on the thinkorswim^{®}platform from TD Ameritrade, as shown in figure 1.

As the underlying moves, however, an option’s delta doesn’t remain constant. It changes. Option gamma says by how much. It’s expressed as delta's sensitivity to a $1 change in the price of the underlying.

Here’s a quick example of option delta and gamma. Let’s say a call has a .35 delta, and .04 gamma. If the underlying were to rise by $1 the call value should rise by its delta, about $0.35. But the delta would also rise, to about .39 (its original delta of .35, plus its gamma of .04). So if the underlying were to rise another $1, the call value should rise by about $0.39.

Delta and gamma work the same way on a $1 drop in the underlying—if a .35-delta call has a gamma of .04, a $1 drop in the underlying would lower its theoretical value by $0.35, and its delta would drop to .31.

Understanding delta and gamma can play a big part in both directional and non-directional trading strategies.

One thing that’s constant is time, and options tend to lose value over time. Theta says by how much. This greek, also known as “time decay” or simply “decay,” is defined as a measure of an option's sensitivity to time decay. So if a call option is worth $2.36 today and it has a theta of .07, then tomorrow—all other things being equal—it will be worth $2.29.

If you owned one of these calls, the option's theta would cost you $7 per option ($.07 times the contract multiplier of 100) to hold the position overnight. If you owned ten, it would cost you $70 per day. The person who is short 10 calls, all else equal, would have a theoretical gain of $70. (Keep in mind that this is theoretical. Any potential profit on a short option position is limited to the credit received when the options were sold).

Time decay is the heart of strategies such as iron condors, calendar spreads and butterfly spreads.

As explained above, option prices are determined by the price of the underlying, the time remaining until expiration, interest, dividends, and volatility. Each of these variables is known at any given point in time except volatility. Sure; we know how much variability a stock has experienced in the past (what traders call "historical volatility"), but no one knows the future. What we can do, however, is look at current prices of options trading in the marketplace, plug in the known variables, and solve for the unknown variable, volatility. It's called implied volatility (IV) because it's the volatility *implied* by the marketplace.

Each option strike and each expiration date might have a different level of implied volatility at any given moment. If the IV goes up, option prices tend to go up. If IV goes down, option prices tend to go down. Vega says by how much, and it’s expressed as a measure of an option's sensitivity to a 1% change in the underlying’s IV.

Let’s say that the call that’s worth $2.36 today has a 30% implied volatility, and the vega of the option is $0.18. If the implied volatility drops 1 percentage point, to 29%, that would correspond to an $0.18 drop in the price of the option ($18 for one option contract). The option price would be *higher* by $0.36 if the implied volatility *rose* 2 percentage points to 32%.

Straddles and strangles are among the strategies that give traders the ability to speculate or hedge against changes in implied volatility.

Understanding the greeks can be a critical step in understanding the potential risks and rewards of options trading.

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- An option's delta and gamma reflect its sensitivity to changes in the price of the underlying
- An option's theta measures how its price changes with the passage of time
- An option's vega reflects its sensitivity to changes in implied volatility

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*Please
note that the examples above do not account for transaction costs or dividends.
Transaction costs (commissions and other fees) are important factors and should
be considered when evaluating any options trade. Transactions cost for
trades placed online at TD Ameritrade are $6.95 for stock orders, $6.95 for
option orders plus a $0.75 fee per contract. Orders placed by other means will
have higher transaction costs. Options exercise and assignment fees are $19.99.*

*Spreads
and other multiple-leg option strategies can entail substantial transaction
costs, including multiple commissions, which may impact any potential return.
These are advanced option strategies and often involve greater risk, and
more complex risk, than basic options trades.*

Market volatility, volume, and system availability may delay account access and trade executions.

Past performance of a security or strategy does not guarantee future results or success.

Options are not suitable for all investors as the special risks inherent to options trading may expose investors to potentially rapid and substantial losses. Options trading subject to TD Ameritrade review and approval. Please read Characteristics and Risks of Standardized Options before investing in options.

Supporting documentation for any claims, comparisons, statistics, or other technical data will be supplied upon request.

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