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The Pyramid Optimizer - Instructions 

General Information

What might be even more profitable (and risky) than options? Let me give you a hint - instead of adding your profits, you multiply them! If you answered "pyramiding", then you've got this one right. The answer is Stock/Index Option Pyramid.

The basic idea is that you buy call options on a stock that you expect to rise. When you achieve a substantial profit on these options, you sell them and use the proceeds to buy call options on the same stock, but at the higher strike price. You can repeat this scheme, as long as the stock does not reach your price objective.

Before we continue with the topic of pyramiding we would like to present you with basic features of this tool, as it can be used in many ways.

The basic use of this tool is to calculate strike price of the option that lets you gain the most on particular move in the underlying equity. Calculations take into the account different commission fees from your broker, so it is realistic. You will see the profitability of the best strike price and the profitability of the ATM (at-the-money) options and you can then decide whether the difference is big enough, to justify the higher risk. For example with 400% and 380% it would make sense to buy ATMs, whereas with 400% and 120% it most likely does not.

The danger in speculation using pyramiding is that you have to be very accurate when it comes to forecasting the range of a particular upswing. Sometimes even if the stock does rise let's say 80% of your predicted range, you can actually lose money. That would be the case if you just bought call options with a high strike price and stocks begins to fall or even consolidating at current level. Your options value will decrease, as each day there is less time to the expiry date. You can decrease the risk by making your price projections really conservative making them more like "stock will rise AT LEAST to this level" instead of "stock COULD reach as high as...".

So, if you've established the amount of capital you want to put into this type of transaction and made conservative price and time projection, there is one more thing that you need to know before putting your money to work - the strikes. Choosing the right strike prices is essential for this transaction to really work. If you choose strikes too close or too far from each other you will not fully take advantage of the enormous profit potential that pyramiding has to offer.

Can we somehow estimate the strikes to maximize the profit? Of course we can! This tool is designed especially for people who want to make the most of their pyramiding strategies.

All you need to do is enter all necessary information and click the "Calculate!" button.

Input Page

The "Current data" section is dedicated to values derived directly from the market, whereas the "Forecasts" section includes values that you forecast or for which you want to make the calculations.

Below you'll find details regarding each box in these sections.

  • Choose the option type- choose the type of option for which the calculations will be made.
  • Current stock prive / index value - this is the current price of the underlying security.
  • The first strike price - the cheapest ITM option strike price - this is the strike price of the cheapest in-the-money option. If the predicted starting price of this particular trade is lower than this strike price, use the strike price, which is just below (call options) or above (put options) that price.
  • The last strike price -  this is the lowest (for put options) or highest (for call options) available strike price for a particular option chain).
  • The difference between strike prices - this is the difference between second available strike price and the first one. For example for GOOG and the options that expire in January 2010 that would be 310 - 300 = 10.
  • Current time to expiry (in days) - days that remain until the expiration date of that option type. Choose the set of options that corresponds to your time forecasts.
  • Risk free rate - the theoretical rate of return of an investment with no risk. In practice, the interest rate on a 3-month U.S. T-bill is commonly used. You can check its current value here.
  • Current bid price of the cheapest ITM option - this is the current bid price of the cheapest of the in-the-money option types. In other words that's the (bid) value of the option, whose strike price is just below current stock price (for call options) or that's the value of the option, whose strike price is just above current stock price (for put options). If the predicted starting price of this particular trade is lower than this strike price, use the bid price of the option, whose strike price you entered in the "First strike price" box.
  • Commission - please choose the way of calculating fees that best corresponds to your broker's commission system and enter appropriate value. If you selected commission in cash, then you have to enter the amount of money (in U.S. cents) you are being charged, when buying or selling one option (by one option we mean the option contract for 1 share). For instance if you pay $12 for a one option (for 100 shares) then it means that the commission per option on one share is 12 cents. In this case, enter 12.
  • Dominant spread - this is the most common spread (difference between bid and ask price) among deep out-of-the-money options. For example at the moment of writing, the call option prices for GG that expire in January 2010 have following bids and asks. At the moment of writing $70 was the highest strike price available. The 0.30 spread is both most common and average value for the deep out-of-the-money options and this is precisely what you should enter in the "Dominant spread" box in this case. If these values differ so much that you are unable to determine most common one, you should be fine by entering the spread for the option with highest (call) or lowest (put) strike price available.
  • Starting price of the underlying security - this is the price of the underlying security at which you want to purchase your first set of options.
  • Initial time to expiry - days that remain until the expiration date of the option type that you wish to buy, at the moment of purchase. For example if you predict a move that will materialize in 30 days, you need to purchase options that have more than 30 days until expiration. If available options expire in 20, 40 or more days, you should use options that expire in 40 days or more. The more distant expiry date you choose, the less risky and less profitable the whole transaction will get. Try different scenarios before making your final decision.
  • Final price of the underlying security -  this is the price of the underlying security that you expect to be reached. When the underlying security reaches this price, you plan to take profits.
  • Days needed to reach the price objective - days you expect this pyramiding transaction to take place - from the day you purchase your first set of options to the day you expect the underlying security's price to reach the predicted value.

After clicking the "Calculate!" button and waiting several seconds you will see the results.

Output Page

The first chart features the temporary valuation of capital used for each of the proposed strategies. Each day the value of money invested in different types of assets changes accordingly to many factors. We have calculated these values by making a few assumptions (which you can find in this document) and applying them along with the data you entered in our models. The results can be seen on the charts. You can see for yourself what implications does switching strike prices have on your portfolio. In this case that would be temporary losing large part of your money but regaining it after a day or two. This would be caused by the fact that we use the price you would get when exiting your position at a given day. As you would probably just have purchased very cheap options, the difference between ask and bid prices is very high comparing to the value of these options – not to mention the commission that would need to be charged. This means that if you bought and sold these options just after that, you would lose very large part of your capital. As the price continues in your predicted direction, the value of the options increases dramatically in both nominal terms and on a percentage basis, making selling extremely more profitable than a few days before.

The second chart presents the column comparison between returns that could be achieved from each type of the investment.

Please note that the scale on the vertical axis on both charts is logarithmic and that the label on it says “Potential revenue (%)“. “Revenue” – not “Profit” – that means that we don’t deduct the initial value of your investment, but rather tell you how much of the initial value would your invested money would your capital be worth after closing your position on a given day. In other words – this is the profit + 100%.

Below these charts you can find the data you entered in the “Forecasts” section, so that you can check if everything was typed in correctly.

Next on the page is the table with detailed results, where you can see details for following types of strategies:

  • Pyramiding composed of 3 different option types - (implying two changes of strike price). Apart from maximum rate of return of this particular transaction, you can find here also more detailed information. We provide you with strike prices that would be optimal to use and at what price of the underlying security you should switch from one option type to another. We also give our thoughts on the probable time when such a price is likely to occur, given your forecasts.
  • Pyramiding composed of 2 different option types - (implying one change of strike price). As above, however this time only 2 different strike prices are taken into account.
  • Using a single option with the strike price that gives you the best return - We check the return for all available option types and choose the one that gives you biggest profits.
  • Using the ATM option -  In practice we check the profitability of the option, whose strike price is most similar to the current price of the underlying stock or value of index.
  • Investing in the underlying security -  It means purchasing stock or shorting it. In the latter case we calculate the rate of return as the profit divided by the original liability created by the act of shorting.

The last part of the results page is the summary.

It’s up to you to decide which strategy you should use. We suggest not to use pyramiding if it does not give you at least twice as much profit as single best option would. The same goes for pyramiding using 3 option types, and 2 options types. Pyramiding works best when price of particular security rises (or falls) dramatically in a relatively short time frame.

Technical Details

Our tool includes the basic Black-Scholes options pricing model. This model was originally designed to price European options, however it is also commonly used to price American options. It can also be used for calculating index options. All assumptions made in this model also apply here.

Please note that one particular assumptions of the Black-Scholes model (the one that says the volatility is constant) may negatively distort calculations, especially in the highly risky and lucrative transactions such as pyramiding.  Should that be the case, market's perception toward assessing volatility would probably change before you would get to switch strike prices. Both options - the one that you would be selling and the one that you would be buying - would be worth more than our models originally forecasted. This might result in overall change in the profitability of the whole transaction; however in our opinion the changes and general implications of the results should not be very significant.

We also assumed that the stock/index rise is stable percentage-wise - the stock's price increases every day by the same amount percentage-wise (for example 1%) instead of the same amount in nominal terms (for example $1). This makes the price projections more realistic.

This tool was designed for educational purposes only and may only be used as such, you use it at your own responsibility.


If you are reading this, you have probably encountered problems while accessing our tools. In order to make our help more efficient, we have prepared a list of common problems that users of the Website may usually have and sorted them in the order of frequency, in which they appear.

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