Introduction to the Greeks

Lesson in Course: Derivatives and options (beginner, 7min)

I understand the basics of call and put options. What are the quantitative levers I need to understand?


What it's about: Greeks are characteristics that distinguish option contracts from one another.

Why it's important: Effective purchasing and selling strategies require understanding the Greeks.

Key takeaway: Out of the 5 Greeks, theta represents time risk.

Investors and everyday traders have spent a great deal of time studying options to understand how to make money with them. Traders and academics have come up with their own code names, named after Greek letters, to describe some basic characteristics of options. Familiarizing ourselves with these concepts will help us learn and retain advanced concepts better. Let's start by watching the 5-minute video below from TD Ameritrade.


Breaking down the Greeks


Delta is the expected price change of our option compared to a change in the underlying stock's price. 

For example, an option with a delta of 0.40 means that for every $1 that the underlying stock increases, the value or the price of the option increases by $0.40. Likewise, a loss of $1 on the stock price results in a $0.40 decrease in the option's price. 

Delta can also be used as a rough estimate of the probability that an option will be in-the-money at maturity. Returning to the same example, a delta of 0.40 can be seen as having a 40% chance of finishing in-the-money. Super out-of-the-money options will have a low delta since there's a very small chance of finishing in-the-money. 

Call option deltas will always be positive,while put option deltas will always be negative




Gamma refers to any expected changes in delta as the underlying price changes and is known as the curvature of an option. 

Not all relationships stay the same over time—this also applies to delta or the relationship between option prices and the underlying stock price. Gamma helps us predict the change in delta as the stock price continues to change. For example, let's say we have an option with the delta of 0.40 and a gamma of 0.05 and the current underlying stock is worth $1 per share. The delta tells us that for a $1 increase in the underlying stock price, our option value increases by $0.40. However, gamma tells us that the next $1 increase means our option will increase by $0.45, or the gamma + delta.

Breakdown of underlying and option price

Delta = 0.40 and gamma =0.05

Underlying +$1, option +$0.40
Underlying +$2, option +$0.40 + $0.45
Underlying +$3, option +$0.40 + $0.45 + $0.50

Gamma is always positive for both put and call option holders and is negative for option sellers.




Theta represents the time decay of options on a daily basis. 

Extrinsic value decays over time and a -0.04 theta means that the option premium drops $0.04 every day even if the stock price holds steady. Theta is zero-sum and its values are always negative when we purchase options and are positive when we write or sell options. The $0.04 lost every day by the holder is gained by the seller of the option. Thus, theta works as a slow transfer of time value from the buyer of the option to the seller of the option through maturity. 

As the holder of an option, we are hoping that a big change in the underlying's price or volatility can offset our theta decay.


For every 1% change in the implied volatility, Vega refers to the change in an option's price.

A vega of 0.03 means that when the implied volatility drops 1%, the option's price will drop $0.03, and vice versa. We can think of vega as the sensitivity of our option to the perceived risk in the future, or the speed at which the stock moves up and down. Vega will always be positive for both put and call options. Options with longer maturity dates have higher vegas since a lot of things can happen between the purchase date and a maturity date that is far away. As an option approaches maturity, vega disappears.


An interesting fact is that vega is not a Greek letter, but is the most widely adopted description of an option's price sensitivity to volatility. The true Greek equivalent is kappa, and in rare cases, kappa is used in place of vega even though they both represent the same thing.


Rho measures the rate that our option price may change in response to a change in interest rates. 

Rho is the least informative Greek since rho differs depending on the underlying and how settlement is handled by the exchanges and clearinghouses. In addition, interest rates don't change very often. As a result, rho is a lot less actionable compared to vega, theta, and gamma. 

Actionable ideas

Understanding how other investors are placing their bets will allow us to make more informed decisions. Whether we are using advanced strategies or just trying to figure out when to sell, being comfortable with the Greeks will give us a leg up. While there are five Greeks in total, theta is the most important Greek for us to get familiar with first. As the holder or buyer of an option, managing theta decay effectively will help us avoid major losses. We also want to avoid very large gamma positions as these options are extremely unpredictable.

In future lessons, we will cover strategies around each specific Greek. Are any of your friends or family members trading options? Invite them today to Archimedes to learn effective strategies together.



What is Delta?

Delta tells us the expected price change of our option compared to a change in the underlying stock's price. 

What is Gamma?

Gamma measures delta's expected rate of change.

What is Theta?

Theta represents the time decay of options on a daily basis. 

What is  Vega?

Vega estimates how much the option's price may change with each one percentage point change in the implied volatility

What is Rho?

Rho measures the rate that our option's price may change in response to a change in interest rates.