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Option Greeks Defined and Theoretical Calculations + Premium Membership Pricing Information

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The option Greeks are a series of calculations that measure the factors that impact our option prices and risk. The Black-Scholes Model can be used to determine the theoretical value for a call or put option based on these factors:

  • Volatility
  • Type of option
  • Stock price
  • Time to expiration
  • Strike price
  • Risk-free interest rate

This article will provide brief definitions of the option Greeks and then use Apple Computer, Inc. (Nasdaq: AAPL) to show how the theoretical value of the Greeks is calculated using an option’s calculator.

Option Greeks defined

  • Delta: The amount an option value will change for every $1.00 price change in the underlying security. It also measures the approximate probability of the option expiring in-the-money or with intrinsic-value. Deltas for calls run from 0 to 1. Higher Delta options have a greater chance of exercise
  • Gamma: The rate of change of Delta, for every $1.00 change in stock price … the “Delta of Deltas”
  • Theta: How much the theoretical value of an option price will change with the passage of 1 calendar day. Time-value of our premiums decline for every calendar day we delay selling the option
  • Vega: The amount an option price will change for every 1% change in stock implied volatility. High IV options imply greater trade risk, but come with higher associated option premiums
  • Rho: Measures the change in an option price due to a change in risk-free interest rates. Not considered a major Greek

Theoretical Greek & option price calculations for AAPL (2/4/2024 – 3/1/2024): Data entries

The 6 factors mentioned above are entered into the calculator.

Theoretical calculations after initial entries ($190.00 call valued at $2.187)

In the next screenshot, a real-life option chain on 2/4/2024 will be analyzed to compare theoretical value versus actual values. The focus will be on the top row (theoretical price, Delta & Gamma)

AAPL: Option chain on 2/4/2024

  • Investors are willing to pay more for the 3/1/2024 $190.00 call (AAPL trading at $185.11 at the time): $2.43 – $2.56 spread versus the theoretical value of $2.187
  • The Delta calculation is similar (0.350 vs. 0.3788)
  • The Gamma calculation is even closer (0.038 vs. 0.037)


Option prices will frequently vary from the theoretical prices generated by Greek Calculators, as investors may be willing to pay more (or less) than these calculated prices. The Option Greeks must be understood (especially Delta, Vega and Theta), in terms of how they impact our option trades. Their specific numerical stats rarely have to be accessed, except in cases where we are taking ultra-low-risk approaches to option trading.

Covered Call Writing Alternative Strategies

Portfolio Overwriting– using stocks in buy-and-hold portfolios.
The Collar Strategy– using protective puts.
The Poor Man’s Covered Call– using LEAPS options.

Covered call writing is a cash-generating strategy that lowers our cost basis thereby improving our opportunities for successful investments. One of the many benefits of incorporating this strategy into our investment portfolios is that the system can be crafted to meet our trading style, market assessment, portfolio net worth and personal risk tolerance. This book details three such covered call writing-like strategies.

Click here for more information and purchase link.

Premium Membership Price Increase Notification: No Rate Increase for Current Members

On September 1, 2024, BCI will be raising membership rates for new members only. This will not apply to current members. It’s been 3 years since we had a rate increase. In that period, we have added dozens of training videos, additional downloads and resources and more quality data to our stock and ETF reports. We are fortunate to have such a robust and expanding membership and strive to provide the best high-quality information and tools at the lowest industry prices.

This price increase will not apply to current active members as you are grandfathered into the current rate for life or as long as your membership remains active. This is our loyalty pledge to you.

The increase for new members will go into effect on September 1, 2024, as follows:

Monthly: $19.95 for the first (trial) month and $69.00 each 30-days thereafter (currently $57.95).

Annual: $778.95 for the first 13 months (includes a reduced first month and a free last month) and then $828.00 every 13 months thereafter (includes 1 free month). Currently $657.40 and $695.40.

All new members who subscribe between now and 8/31/2024 will be grandfathered into the current rate and will see no price increase on 9/1/2021.

Thanks to all our loyal members for your support over the past 17 years and for putting BCI on the financial map.

Click here for member benefits video.

Click here for membership information.

Your generous testimonials

Over the years, the BCI community has been incredibly gracious by sending our BCI team email testimonials sharing stories as to what our educational content has meant to their families. Moving forward, we have decided to share some of these testimonials in our blog articles. We will never use a last name unless given permission:

Hi Alan, Hi Barry,

I want to thank you and your team for the work you are doing to help hard-working blue collar investors like me. I stumbled onto your website approximately the second week of December of 2023. I was immediately hooked. Your systematic, methodical approach to covered call trading was intensely appealing to me. 

I am currently paper trading, an just closed out my first monthly contract trades (yesterday). I am happy to report that my CEO strategy for the contract month which ended today returned a very respectable 1.5%, right in the middle of the 1-2% that you said was achievable. My stock strategy returned a whopping 3.62% (I know that this will not happen every month).     

Once again, thank you very much for the work you do.

Very Best Regards,



Upcoming events

1. BCI-Only Webinar (Zoom)

July 18, 2024

Register here.

Exit Strategy Choices After Exercise of Cash-Secured Puts

When we sell cash-secured puts, we are undertaking the contractual obligation to buy shares at the strike price by the expiration date. Typically, we only sell puts on elite-performers that we would be agreeable to own in our portfolio.

This presentation will analyze 4 potential exit strategy opportunities to consider should the put option be exercised. Information on the following strategies will be highlighted:

  • Selling the stock
  • Holding the stock in our long-term buy-and-hold portfolio
  • Write a covered call (PCP or “wheel” strategy)
  • Implement the Stock Repair Strategy

In addition to these strategies, the following topics will also be included in the webinar:

  • Option basics for selling cash-secured puts
  • Option basics for covered call writing
  • Real-life examples
  • Calculations using the BCI Trade Management Calculator (TMC)
  • Event super discount offer

There will be information offered to all levels of options trades, from beginners to advanced.

A live Q&A will follow the presentation. Attendees can ask any questions related to covered call writing or selling cash-secured puts.

Register here.

2. Investment Masters Symposium (live, in person event)

August 1, 2024

Presentation #1: 8:45 AM – 10:45 AM

Paris Hotel, Las Vegas

Register here.

Covered Call Writing & Selling Cash-Secured Puts to Generate Consistent Cash Flow

Basic & advanced principles for trading low-risk stock options with capital preservation in mind

This presentation will detail stock selection, option selection and position management, the 3 required skills to become elite covered call writers and put sellers. It will also include ultra-conservative approaches to these strategies using Delta and implied volatility to create statistically beneficial trades. Rules and guidelines will be discussed to take the emotions out of our trades resulting in high-probability positive outcomes.

Detailed analysis will be provided regarding how to craft our trades to the current market environment, personal risk-tolerance and strategy return goals.

A multi-tiered option-selling strategy which combines both covered call writing and selling cash-secured puts will also be examined. It is known as the PCP (put-call-put) or “wheel strategy.”

Attendees will be introduced to a one-of-a-kind trade management tool, the Trade Management Calculator, which is used to enter, manage and generate final realized and unrealized trade results.

The course is structured to benefit both beginner and advanced option traders, using real-life examples to enhance the learning process.

Presentation #2: All Stars of Option Trading Event

Register here.

3. Stock Traders Expo- live event in Orlando Florida

October 17 -20

Details to follow.

Alan speaking at a Money Show


15 Responses to “Option Greeks Defined and Theoretical Calculations + Premium Membership Pricing Information”

  1. Barbara June 15, 2024 7:16 am #


    In last week’s sample trade with QQQM, the price went up higher past the OTM strike. I was wondering if any exit strategy steps were taken? I also have covered calls on that one.

    Thanks very much.


    • Alan Ellman June 15, 2024 12:43 pm #


      Not yet. I’m waiting to see how QQQM opens on Monday. If it continues to accelerate, the mid-contract unwind exit strategy may come into play, although it’s late in the monthly cycle.

      Glad you’re in this one.


  2. Barry B June 15, 2024 10:33 pm #

    Premium Members,

    This week’s Weekly Stock Screen And Watch List has been uploaded to The Blue Collar Investor Premium Member site and is available for download in the “Reports” section. Look for the report dated 06/14/24.

    Be sure to check out the latest BCI Training Videos and “Ask Alan” segments. You can view them on The Blue Collar YouTube Channel. For your convenience, the link to the BCI YouTube Channel is:

    Reminder: Premium Member’s pricing is locked into your current rate and you will never see a rate increase as long as the membership remains active.

    Barry and The Blue Collar Investor Team

  3. Marilyn June 16, 2024 12:32 pm #


    I’ve been using the TMC for all my covered call trades. Thanks for this great tool.

    I will sometimes add a protective put to my trades making it a collar trade.

    Is there a way I can use the TMC for collars?

    Thanks for any guidance.


    • Alan Ellman June 17, 2024 6:11 am #


      Yes, the TMC can absolutely be used for our collar trades.

      In the column titled “Entry Call Option Premium”, enter the net option credit (call premium credit minus the put option debit). Make a corresponding notation in the Trade Journal describing the trade.

      I set up a hypothetical example in the screenshot below:

      -Buy BCI at $48.00
      -STO a $50.00 call at $2.00
      -BTO a $45.00 put at $1.00
      -Net option credit is entered at $1.00 ($2.00 – $1.00)
      -Initial time-value return is 2.08%; 23.04% annualized (brown cells)
      -Components of this collar trade is entered into the Trade Journal section of the spreadsheet

      The short call is the main leg of the trade that may require management.



  4. Alan Ellman June 16, 2024 3:28 pm #

    Premium members,

    Since NVDA split 10-for-1 recently, many more of us can now implement this stock in our option-selling portfolios, if we deem it appropriate.

    I’ll be using NVDA in this week’s sample trade and sending it to you Wednesday evening after publication of our new ETF Report.


  5. Charlie June 17, 2024 2:55 pm #


    I’m thinking of the CEO strategy.

    I know there are no earnings dates to worry about but are there ex-dividend dates?


    • Alan Ellman June 18, 2024 6:27 am #


      Yes, the Select Secor SPDRs do generate dividends and, therefore, have ex-dividend dates, which occur on the same day for all of them.

      However, when using our CEO strategy, ex-dividend dates do not play a role as they might when leveraging low cost-basis stocks in non-sheltered option accounts.

      Ex-dates are the main reason for early exercise, although extremely rare. Our concern, in these instances, is for low cost-basis stocks being sold and incurring negative capital gains consequences.

      This is not the case with our CEO strategy, where we purchase these securities each month (or week) and our portfolio content often changes based on best-performers each contract expiration.

      Let me take this a step further. If early exercise where to occur with CEO, I’m a happy camper. This means that we have maximized our current trade and now have the cash back from the sale of the shares and (perhaps) can enter another trade with a new underlying ETF (based on our current ETF Report), to generate a 2nd income stream in the same contract cycle with the same cash investment.

      Bottom line: Yes, the Select Sector SPDRs do have ex-dividend dates, but there is no need to avoid them.


  6. Charlie June 19, 2024 5:08 pm #


    When you roll an option, do you do each trade individually to optimize price, or one combined trade



    • Alan Ellman June 20, 2024 6:28 am #


      2 trades. The BTC and then the STO immediately after closing the near-term contract position. If we have the opportunity to leverage the “Show or Fill” rule, and “negotiate” better prices with the market maker, we always take advantage of those situations.

      Before we roll, we check the calculations to make sure they align with our pre-stated initial time-value return goal range. If yes, we are ready to take action and roll the option.


  7. Alan Ellman June 19, 2024 9:21 pm #

    Premium members:

    This week’s 4-page report of top-performing ETFs, along with our sample trade of the week, has been uploaded to your premium site. The Select Sector SPDR section is now crafted to align with our streamlined (CEO) approach to covered call writing. The report also lists Top-performing ETFs with Weekly options, mid-week market tone as well as the implied volatility of all eligible candidates.

    We have also included a sample trade taken from one of our BCI watchlists.

    Premium member video link:

    For your convenience, here is the link to login to the premium site:

    NOT A PREMIUM MEMBER? Check out this link:

    Alan and the BCI team

  8. Michael June 20, 2024 1:44 am #


    In this video:

    Is there a technical analysis explanation how you decided on the $40 strike price.


    • Alan Ellman June 20, 2024 6:15 am #


      Technical analysis is used in the stock screening process. We use trend and momentum indicators, as well as volume as 1/3 of our screening requirements. Fundamental analysis and common-sense screens (like minimum trading volume etc.) are the other 2/3.

      Now, let’s focus in on strike selection. First, we decide on the “moneyness” of the strikes (in-the-money, at-the-money or out-of-the-money). We use ATM and OTM in normal to bull markets and ITM in bear and volatile markets.

      I am currently bullish on the market, so I selected a slightly OTM strike (40.00). As far as which OTM strike, we must first identify our initial time-value return goal range … how much money are we seeking to generate when we craft our trades?

      For me, it’s 2% – 4% for a monthly trade. In this case, a 3.27% initial time-value return was generated. We then enter our 20% BTC GTC limit order (as shown in the video) and we put on our position management caps.


  9. Alan Ellman June 20, 2024 11:23 am #

    Premium members:

    The Blue Chip Report of the best-performing Dow 30 (DJI) stocks has been uploaded to your member site.

    Due to the fact that the S&P 500 is outperforming the Dow 30 so substantially, there are only 3 stocks that meet our “eligible” requirements.

    The 1-month comparison chart below demonstrates the stark difference in price performance of the 2 benchmarks over the past 1-month. Similar charts can be created for 3- and 6-months, as well.



  10. Alan Ellman June 21, 2024 6:22 am #

    CMG stock price:

    On 6/26, Chipotle will split 50-for-1. Based on the current price, shares will be trading about $64.00 per share instead of the > $3000.00 per share today. About time!

    CMG is currently a bold stock on our watchlist.


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