Breaking Down Option Greeks

In this tutorial, I will introduce the concept of option greeks.

What are the "Greeks"?

"The Greeks", in the context of options trading, refers to the different types of dimensions or types risk involved when taking an option position.

They are called "The Greeks" because each risk variable is associated with a greek letter.

Every serious options trader should strive to gain a deep understanding of the greeks since they are widely used when assessing the risk of an option trade/portfolio.


A high level overview

There are a wide variety of greeks, including but not limited to:

  • Delta
  • Gamma
  • Vega
  • Theta
  • Rho

The primary Greeks (Delta, Vega, Theta, Gamma) are simply a first partial derivative of the the options pricing model.

These Greek indicators change over time, therefore it is important for traders to be aware of them in order assess how their portfolio may be affected.


Delta measures the rate at which the value of the option changes with respect to a change in price of the underlying asset.

Delta helps answers the following question:

How much will the value of option XYZ change if the price increases/decreases by 1$?

For example, if an option has a current delta of 0.5 and the underlying asset price increases by 1$, the value of the option would increase/decrease 0.5$.


Theta measures the sensitivity of the option value with respect to time.

Theta helps answer the following question:

For each day that passes, how does that alone affect the value of the option?

Example: If an investor buys an option with a theta of -0.50, that means the option value decreases by 50 cents each day all else equal.


Gamma represents the rate of change between an option's delta and the underlying asset's price. For all you Math Connoisseur's this is simply the second partial derivative of the options pricing model with respect to price.

In other words, Gamma tells us how delta changes with respect to a change in price.

Example: assume an investor is long one call option on hypothetical stock XYZ. The call option has a delta of 0.50 and a gamma of 0.10. Therefore, if stock XYZ increases or decreases by $1, the call option's delta would increase or decrease by 0.10.


Vega tells us how the option value changes with respect to a change in the underlying asset's implied volatility.

Vega helps us answer the question:

How much will the value of XYZ option change if the implied volatility increases by 1%?

Example: An option with a Vega of 0.10 indicates the option's value is expected to change by 10 cents if the implied volatility changes by 1%.


Rho indicates the rate of change between an option's value and a 1% change in the interest rate.

Rho helps us answer the following question:

How much will the value of my option change if the interest rate increases by 1%?

Example: assume a call option has a rho of 0.05 and a price of $1.25. If interest rates rise by 1%, the value of the call option would increase to $1.30, all else being equal.

Other Greeks

There are other greek that are not as widely used as the ones discussed above. These include:

  • Lambda
  • Epsilon
  • Vomma
  • Vera
  • Speed
  • Zomma
  • Color
  • Ultima

These greeks are mainly second or third derivatives of the pricing model. They are becoming more used as computer software can help compute the values of these abstract risk factors.


  • "The Greeks" refers to the varios types of risk that an option position involves.

  • Greeks are used by option traders and portfolio manager in order to assess the risk of their portfolio/position.

  • The most common greeks include: Delta, Gamma, Theta, Vega. These are basically partial derivatives of the Black-Scholes option pricing model.