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Option Master Chapter 5
Download the Option Master Manual - PDF 187k


Software for Pricing Options
by Kenneth R. Trester
and Robert P. Swanson

Chapter 5 - What Are Your Odds of Profiting?

Measuring Probability of Profit

One of the most valuable features of OPTION MASTER® is its ability to determine your probability of profit when you buy or write an option or enter an options strategy. Such information can be indispensable when deciding whether to buy or write an option or to enter a spread. For example, sometimes buying an options looks like a good play, but once you see your probability of profit, you may change your mind, as it may be too low. So these probability figures may help you avoid errors in the option markets.

Probability of profit is defined as your chances of profiting if you hold an option until expiration in a random market. What the program does is calculate the area under a log normal curve determined by the price volatility of the underlying stock, index or futures contract.

Whenever you calculate the theoretical value of an option, OPTION MASTER® also determines your probability of profit if you bought the option at the theoretical price. Of course, if you subtract the probability of profit from 100, you will determine your chances of profiting at the theoretical price, if you are the option writer. For example, if the probability of profit is 30%, then your chances of profiting if you are an option writer is 70% (100 - 30 = 70).

When you wish to measure the probability of profit for an option you are considering buying at its actual market price instead of its theoretical price, you will be required to enter the actual option price.

An invaluable feature of the Probability of Profit module is your ability to measure the probability of profit of an option strategy you design. To measure the probability of profit, you will need to provide the break-even price for the strategy. The break-even price is the underlying stock, index or futures price at which you either begin to make a profit with, for example, a debit spread, or an option buying strategy where the stock or futures hits your profit goal. Or, the break-even price can be the stop-loss price for a naked writing position, or a credit spread. Here, you will begin losing if the stock or futures price reaches the break-even point. In such cases, the probability or profit will be the reverse of the figure generated. OPTION MASTER® gives you the chance of reaching the break-even price.

With credit spreads or naked writing, you profit if the break-even price is not reached. Therefore, you should subtract the probability of profit from 100 to determine your chances of profiting with credit spreads or writing strategies.

Using the Probability of Profit Module

Let's go through a few examples to demonstrate how to measure probability of profits. First, we will determine the probability of profit if you buy a long-term Southwest Airlines (LUV) January 1997 put with a strike price of 20, purchased on August 4, 1995 at 3/4 when the stock was priced at 28 5/8 with a volatility of 43%.

Click on the Calculate menu item, then select Probabilities, then select Stock or Index Options under the title Probability of Profit. Enter the Beginning Date of August 4 and Expiration Month at January, 1997. Now enter the Stock Price, 28.63, Strike Price, 20, and a Volatility, .43. Finally, enter the Option Price, 3/4, in the appropriate entry box. Click or Tab to Put Prices, hit the Enter key and you will see the Probability of Profit of 21% along with the Delta, Gamma, Theta and Vega. (Refer to Figure 14)

Now let's determine the Probability of Profit of buying a December Silver 5.75 call option that is priced at 10.7¢ with the December Silver futures priced at 526.9, and Historical Volatility of 24% on August 7. Again, move to the Probability of Profit title under Probabilities and select Futures Options. Again, use a Beginning Date of August 7, then enter the Expiration Date which, for the December Silver futures was November 10, 1995. Now enter the Futures Price, Strike Price, and Volatility and the Option Price in the appropriate entry boxes using the Tab key to move from one box to another. Then click on Call Prices and check your results in the Message Center. (Refer to Figure 15) The Probability of Profit line is 20%.

Now let's develop an index option strategy where you have written an August S & P 100 (OEX) index call option naked or entered an August OEX call credit spread where you have set a Stop Loss of 545 on the OEX, so that if the OEX hits its 545, you would exit your position. The OEX present price is 531.11 on August 7 with a Historical Volatility of 11%.

What are your chances of hitting your stop-loss of 545 before August expiration? Select the Probabilities menu, then select Stock or Index Options under the title Other Strategies. Then enter a Beginning Date of August 7 and an August Expiration Month. Now enter the S & P 100 Index Price of 531.11 in the Stock Price entry box. Now tab to the Breakeven Price entry box and enter the Stop Loss price of 545.

OPTION MASTER® will tell you the probability of being at or beyond the price placed in this Break-even entry box at expiration. Now enter the Volatility of 11% and click on Call Prices because this stop-loss price is above the present price of the OEX. In this case, your chances of the OEX being beyond the Stop-Loss at expiration would be only 9%. (Refer to Figure 16)

The Other Strategies section enables you to measure your chances of being above or below a specific stock, index or futures price (the Breakeven Price entry only box) at expiration. This feature is quite useful as you plan out your option strategies. The Probability of Profit figure is dependent on the Volatility figure that you use. But also be warned that with a good volatility number, the Probability of Profit estimates are more accurate than you think. Don't let your emotions allow you to disregard these probability figures.

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