The Option Trader’s Two Best Friends

04/28/2011 7:00 am EST


Option Greeks Delta and Theta, when used correctly, can help traders to manage risk by clearly stating how sensitive an option is to changes in the underlying asset and the passage of time.

The world of investing is often a tricky place to play, quick to punish the ignorant and sometimes slow to reward even the knowledgeable.

Making the jump from simple stock trading to the complex world of options trading is like moving to a foreign country. You’re immersed in a culture with not only new rules, but also a whole new language.

For those yet to fully embrace option trading, consider this a primer on the language of options.

Not only are the option “Greeks” considered the language of options, they’re also a risk manager’s best friend. Simply put, the Greeks measure risk. They offer the ability to identify how much money is on the line at any given time.

See related video: Option Traders Need the Greeks

Consider the unfortunate plight of a new option trader unaware of how to quantify risk. While reviewing a long call option position, their thoughts may go something like this:

“Since I bought a call option, I will make lots of money if the stock increases in value. I’m not sure how much, but I will profit. On the other hand, if the stock drops in value, I will lose money. I know I paid $1,400 for the option, so I can’t lose more than that, but I’m just not sure how quickly I’ll lose it. I will also lose money as time passes. I wonder how much I will lose? And of course, there’s the volatility component I heard of. If implied volatility drops, my option will also fall in value. I’m not sure how much though….”

Notice how many times the phrase “how much” comes up. How much do I lose if the stock moves, if time passes, if volatility changes? These are essential questions to answer if one truly wants to understand risk.

But unlike the many mysteries of the universe, these are questions that are readily answerable. Look no further than the Greeks, the providers of answers to the option trader’s everyday “how much” questions.

While there are four common Greeks—Delta, Theta, Vega, and Gamma—today’s discussion will focus on Delta and Theta.

NEXT: Using Delta and Theta to Minimize Risk



Delta, the fourth letter of the Greek alphabet, is typically the first Greek option traders become acquainted with. Initially, most traders learn Delta can be used to measure the rate of change of an option.

A review of option pricing illustrates that a rise in the stock price increases call option premiums and decreases put options. Delta measures exactly how sensitive an option is to movements in the underlying stock price.

More specifically, it measures the change in an option’s value given a $1 increase in the underlying. Like the other Greeks, Delta can be either positive or negative. Bullish positions have positive Delta values, while bearish positions have negative ones. Here’s a handy table:

Click to Enlarge

Delta ranges between 0 and 100. Since most option chains list Delta on a per-share basis, a positive 50 Delta will be listed as .50, and a negative 50 Delta will be listed as -.50.

In-the-money options generally have Delta values greater than 50. At-the-money options have Delta about equal to 50. Out-of-the-money options have Delta less than 50.

As options move deeper in the money, the Delta will approach 100, and as they move further out of the money, the Delta will approach zero.

Understanding Delta as the rate of change enables us to forecast how much an option should change in value given a certain price movement in the underlying stock.

Suppose XYZ stock is currently trading at $131, the 125 strike call option has a Delta of .80, and the 135 call option has a Delta of .25. 

If XYZ increases from $131 to $132, the 125 call option should increase in value by $0.80. The 135 call option should increase in value by $0.25.

Because put options decrease in value as the stock rises, let’s see how the 125 and 135 puts would have fared. The 125 put has a Delta of -.19 and the 135 put has a Delta of -.74.

The $1 rise in XYZ (from $131 to $132) would have caused the 135 put to decrease in value by $0.74 and the 125 put to decrease in value by $0.19.


Options are decaying assets. That is to say they lose value as time passes, a phenomenon referred to as “time decay.”

Want to measure the rate of decay? This is where Theta, the eighth letter of the Greek alphabet, comes into play. Theta simply tells you how much money an option will lose per day.

Theta can either be your friend or foe. When buying options, time decay is an unfortunate foe that must be dealt with. We say that your position is “negative-Theta” since you’re losing money due to the passage of time.

When selling options, however, time decay is a fortunate friend that can help you accumulate profits over time. Your position is said to be “positive-Theta” in those cases.

Like Delta, Theta is also listed on a per-share basis within an options chain. If you purchased an option with a Theta of -.45, you would be losing $0.45 per share per day. Since one option contract controls 100 shares, your total loss would come to $45 per contract.

When entering negative-Theta trades such as a long call option, traders hope to make more money due to a favorable move in the stock price or volatility than what they lose due to time decay.

Theta increases exponentially as options approach expiration, which is why most experienced traders avoid holding short-term options.

On the other hand, when entering positive-Theta trades, traders tend to sell short-term options in order to exploit the higher rate of time decay. This is why the majority of option selling strategies, such as covered calls, naked puts, and calendar spreads involve selling front-month options.

With a proper understanding of Delta and Theta, you’re not only one step closer to risk management mastery, but also becoming fluent in Greek…at least two words worth!

By Tyler Craig, trader and blogger,

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