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The 6-Week Options Trading Kickstarter: Meet the Greeks!


Steve Smith breaks down delta, theta, vega, gamma, and rho.


Editor's note: To help investors get their feet wet with options trading, Minyanville has launched this "6-Week Options Kickstarter," an educational series aimed at increasing understanding of the basic nuts and bolts of options. In this series, veteran options trader Steve Smith will take you through options fundamentals with an emphasis on real-world applications. Note: Intermediate or advanced-level traders may get more mileage out of Minyanville's 9 Weeks to Better Options Trading series.

In any endeavor, whether in business, law, medicine, sports, or even parenting, a certain amount of jargon becomes the lingua franca among active participants. It helps people express complex concepts in a concise manner. It also often serves the second purpose of making the "professionals" feel more important and knowledgeable than the laypeople.

The options industry is no exception.

Last week, we discussed how options get priced or valued using the five variables of the Black-Scholes model.

This week, we'll look at "the Greeks," which are used to define how an option's price will change relative to certain variables. And we're going to do it in plain English by using the commonly applied applications as opposed to the strict mathematical definitions.

The five Greeks are: delta, theta, vega, gamma, and rho.

We'll start off by focusing on the three most important ones:


Delta is the expected change in an option's price for every $1 move in the price of the underlying stock. Delta can range from 0.00 to 1.00, with calls being expressed as a positive number and puts as a negative number. The rule of thumb is that an at-the-money option has a delta of 0.50.

It is very important to understand that delta is not fixed. It is a function of the underlying stock price and the time remaining until expiration. As an option moves further into-the-money and time decays, the delta increases at an accelerated rate. Conversely, as an option moves further out-of-the-money and has more time remaining, delta decreases at a slower rate.

For example, if shares of Apple (AAPL) moved from $615 to $625, you could expect the at-the-money $610 call to increase by about $6 per contract, and the at-the-money $615 put to decline by about $4 per contract.

On the call side, a delta of 0.50 would suggest a $5 move, but since delta is on a slope, it increases for call on the way up, pushing the move up to $6. Conversely, it decreases on the way down for puts, so the put only declines by $4.

This is a valuable feature of options in that your profits will accelerate as price moves in your direction and losses will decelerate relative to the stock as price moves against you – so profits can pile up faster than losses.

Another important reason to understand delta is that it will help you gear expectations and determine how many contracts might be needed to hedge a stock position.


Theta is the expected percentage change in an option's price for a one-unit change in time. Options are a decaying asset in that their value decreases as time passes. This can work in your favor if you are short an option, or against you if you are long an option.

Theta, or time decay, is not influenced by any of the other variables, but it is defined on slope. That is, it accelerates as expiration approaches. You can look back at last week's article on options pricing for a more in-depth discussion of how theta is defined on a square root.

For example, the at-the-money $20 call for Fusion-io (FIO) that has 30 days remaining and expires on August 18 has a theta of -0.03, meaning the call option will lose $0.03 of value for each day that passes. With the option priced at $1.70, that is 1.76% of decay per day. By the time there is only one week, or seven days until expiration, that option will be losing $0.05 per day in time decay, which on the then-expected price of $0.68 per contract, represents 7% decay per day.

These numbers assume all other variables, such as stock price and implied volatility, remain the same. You can play with various time frames and inputs using this options calculator.


Vega is the expected change in an option's value for a one-unit move in implied volatility. Again, the strict formula is defined as a 1% move, but for practical purposes it will typically be expressed in dollars per one-point move.

Let's see if we can put these three Greeks together.

Last Thursday, Google (GOOG) closed at $593 prior to its earnings release. The August $600 call had a value of $16.80 per contract. Its delta was 0.46 and its theta was 0.35.

The implied volatility was 29.5% and the vega was 0.66.

On Friday, following the earnings report, shares rose $17 to trade at $610. Based on the delta and theta, we'd expect the $600 calls to gain around $7.80 and be trading around $24.60 per contract. But at midday, those calls were trading around $20 per contract. The $4.60 discrepancy can be attributed the fact that implied volatility dropped eight points to 21.5%. So with a vega of 0.66, that would translate to $5.28 in lost value (8 x 0.66 = $5.28). The increase in delta from 0.46 to 0.64 helped to offset some of the decline in implied volatility.

Again, using the options calculator is a great way to play out various scenarios.

We'll end with a quick dismissal of the last two Greeks.


Rho is the expected change in an option's price for every one-unit change in interest rates. With rates near zero and not going much higher for the foreseeable future, this will not have much of an impact on options pricing.


Gamma is the rate of change in an option's delta for every one-unit change in the price of the underlying. As such, it is a derivative of a derivative (a second derivative) and moves in miniscule increments. This can be an important tool for professionals who engage in hedging and maintaining delta-neutral positions across large multi-strike options positions, but it is beyond the scope of this series.

Here is a full schedule for The 6-Week Options Trading Kickstarter series:

1. What Are Options, and Why Should We Care About Them?
2. Option Pricing Basics
3. Meet the Greeks
4. How to use Options: Three Basic Principles
5. Covered Calls
6. Hedging, Portfolio Protection, and Avoiding Disaster

Twitter: @steve13smith

For more from Steve Smith, take a FREE 14-day trial to OptionSmith and get his specific options trades emailed to you along with exclusive access to his full portfolio. Learn more.
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