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
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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