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Introduction to the Greeks

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

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

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. 


The takeaways for this lesson are:

  • Familiarize ourselves with the different greeks
  • Understand which ones are the important ones

Familiarizing ourselves with these concepts will help us be able to learn and retain advanced concepts better. Let's start by watching the 5-minute video below from TD Ameritrade.

Breaking down the Greeks


Delta tells us 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 the underlying stock increases, the value or the premium 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 premium. 

Delta can also be used as a rough estimate of the probability assigned by traders 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 tells us of any expected changes in delta. 

Not all relationships stay the same over time—this also applies to delta or the relationship between option premiums 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 increased 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 premium

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



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

Extrinsic value decays over time and a -0.04 theta means the option loses $0.04 in premium every day even if the stock price holds steady. Theta values are always negative when we purchase options and are positive when we write options. So theta works as a slow transfer of time value from the buyer of the option to the seller of the option through maturity.

As an option buyer, the only way to counteract theta is if the change in the underlying stock price brings the option more in-the-money. 


Vega tells us the relationship between our option value and achange in the implied volatility.

A vega of 0.03 means that when the implied volatility drops 1%, the premium 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. Vega is easily confused with delta since they both tell the relationship between the value of stock options and the market sentiment. The important difference is to remember is that implied volatility or IV could change while the current stock price remains unaffected.

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.


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

Rho is the least important greek as interest rates don't change often. The Federal Reserve has been very deliberate at increasing or cutting interest rates at a slow and steady pace. As a result, rho has a very minimal impact on our options. 

Understanding how other investors are placing their bets will give us an advantage. Whether we are implementing hedging strategies or just trying to figure out when to sell out and take profits, being comfortable with the Greeks will give us a leg up. Theta is one of the most important Greeks for us to understand and managing theta decay effectively often can help us avoid major losses. This lesson is just the start of the concept and is meant to provide us basic we can revisit. Future lessons 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 premiums may change with each one percentage point change in the implied volatility

What is Rho?

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


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