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Software for Pricing Options
by Kenneth R. Trester
and Robert P. Swanson
Chapter 3 - Using OPTION MASTER®
Quick and Easy
The OPTION MASTER® computer program is designed to quickly
price options for you with few entries, and it is designed for
great ease in use. After fifteen to thirty minutes of practice,
you will discover OPTION MASTER® to be easy-to-use and
understand and you probably will rarely have to resort to reading
this manual after a few sessions of practice.
The goal of our program is to allow you to enter the fewest
key strokes possible so that you can quickly price many options
within a short period of time, or determine your probability of
profit when you buy or sell an option or enter an option
strategy.
In addition, there is a volatility calculation so that you can
calculate the price volatility for the underlying stock, index or
commodity futures contract, which is one of the required inputs
in this program.
A Practice Session
To demonstrate the features of OPTION MASTER®, we will walk
through several examples using the different features of OPTION
MASTER®. The figures used are from OPTION MASTER® for
Windows/TM. OPTION MASTER® for DOS is identical to OPTION
MASTER® for Windows/TM, except for slight differences in
graphics. The current version of OPTION MASTER® for Macintosh®
also operates in a similar fashion to OPTION MASTER® for
Windows/TM, but does not include all of the OPTION MASTER® for
Windows/TM features.
Pricing An Option
Let's assume that you wish to determine the fair Theoretical
Value for a call option on a specific stock, such as IBM, in this
case, the IBM September 110 call, with IBM priced at 105 3/8,
with the present date being August 5, 1995. For a single stock or
index price, go to the menu item, "Single Option
Price." You can do this by clicking on Calculate,
then Prices and finally Single Option Price. There
are six entries that are required:
- Beginning Date (today's date)
- Expiration Month
- Stock Price (stock or index price)
- Strike Price
- Volatility
- Interest Rate (3-month Treasury Bill rate)
The Beginning Date is usually today's date, and your computer
should default automatically to that date. Now, using the tab
key, move to Expiration Month. You can select the month by
clicking on the "arrow" or using the arrow keys, or by
just typing the first letter of the month.
Now move to the Stock Price entry box using the tab
key. Enter the IBM stock price, 105 3/8. You may use the decimal
instead of a fraction if you wish (i.e., 105.37). Now move to the
Strike Price entry box and enter the strike price of 110.
Next, tab to the Volatility entry box. Volatility (the
amount the price will move up or down within a specific time
span) refers to the historical price volatility of the underlying
stock, index or commodity. OPTION MASTER® will calculate the
Historical Volatility in the Volatility menu item of the
program (refer to Chapter 4).
As a rule of thumb, you can enter .30 for a stock with average
price volatility, .20 for a stock with low price volatility, and
.45 for a stock with high price volatility.
Broad-based indexes have price volatilities that range
from .07 to .15. These volatilities are quoted in percents, so
.07 is 7%.
Commodity and other futures contracts vary dramatically. For
example, Treasury Bonds usually have a volatility of around 8%.
Currencies usually have volatilities from 5% to 13%. Treasury
Bills or Eurodollars have a volatility of between 1% and 2%. The
volatility for grains usually ranges from 10% to 40%, pork
bellies 30% to 40%, gold 10% to 20%, silver 20% to 30%. (Refer to
Chapter 4 for typical volatilities.)
With our IBM example, we use a volatility of 30%, or .30. The
program always defaults to this volatility.
Finally, using the Tab key, move to the Interest Rate entry
box and enter the 3-month Treasury Bill rate, or the prevailing
short-term interest rate (i.e., 5% = .05).
Now you are ready to calculate the fair Theoretical Price for the IBM
September 110 call. Just click on the Call Prices box and the results
will be displayed in the Message Center. (Refer to Figure 2)
As you can see, the Theoretical Call Price is 2 5/8. Your
Probability of Profit, if you purchased this option at its
theoretical price, is 26% if held until expiration. If you are an
option writer, your Probability of Profit would be the inverse of
this figure. In other words, you subtract the 26% from 100%,
giving you a Probability of Profit of 74% (100 - 26 = 74).
OPTION MASTER® also displays the Delta, Gamma, Theta and Vega
that are defined in Chapter 2. Once you have the
theoretical price for an option, you can compare it to the actual
price in the market through the newspaper, your quote system, or
your broker.
Pricing Several Options
Now let's say that you want to determine the theoretical price
for a whole group of options for three expiration months. Let's
use the S & P 500 Index (SPX) options in this example with
the SPX at 559.02 and a volatility of 11%.
First click on Calculate, then select Prices and
then select Multiple Option Prices. On the Multiple
Stock & Index Option Prices screen, Beginning Date
is again today's date, here August 5, 1995. Clicking on the arrow
next to the Expiration Cycle gives you the choice of
"every month" -- the next three months, or the months
in the January expiration cycle, the February expiration cycle,
or the March expiration cycle. We will select Every Month.
Next to Stock Price, enter the S & P 500 Index price
of 559.06. The Beginning Strike Price requires the lowest
strike price that you want to determine option value. Enter 540
in this entry box. Tab to Ending Strike Price and using
the arrow key, select a strike price of 575 -- the highest strike
price on which you wish to price options. Tab to Volatility
and enter .11. Then tab to Interest Rate and enter .05.
Always make sure to tab out of an entry box before doing a
calculation.
Now by clicking on Put Prices (or Call Prices), you receive
a whole range of theoretical option prices. (Refer to Figure
3 and Figure
4)
This table of theoretical index put option prices in Figure 4
can then be printed for future reference.
Calculating Futures Options Prices
Entries to determine the theoretical price for a commodity
option differ in several aspects from pricing stock
options. First, you must enter the exact date that the futures
option expires.
The options on a specific commodity expire at a different time
in the month than other commodity options, usually in the
previous month to the futures contract. You can obtain a calendar
that spells out the expiration date for each set of futures
options from your commodity broker. Such a calendar is also
published in Futures magazine.
When entering the futures price and strike price, make sure to
follow the example that accompanies the computer prompts. When
entering grain prices such as wheat, corn or soybeans, enter the
price as cents, rather than dollars and cents. For
example, if September wheat is priced at $4.01 a bushel, enter
401 -- not 4.01. When entering prices for other
commodities such as hogs or cattle, enter the cents per pound as
a whole number. For example, if September hogs are priced at
49.23¢, enter the price as 49.23, not .4923. Currencies
would also be entered as whole numbers for cents. For example, if
the Japanese Yen is priced at .6824 per 100 Yen, enter 68.24 -- do
not enter .6824.
When entering strike prices, follow the same format and
be consistent. If you enter 400 for the futures price and 4.00
for the strike price, the theoretical option price would be way
out-of-line. Therefore, rather than give you a faulty price, the
program gives you an error message.
Entering bond prices is different than other futures
contracts. You enter bond prices in points and 32nds. Therefore,
to enter 90 18/32, you would enter 90 18/32 or 90.18. OPTION
MASTER® converts the 90.18 into 90 18/32 automatically.
Another Practice Session
Let's determine the fair theoretical value of the Soybean
November 650 call on August 3, 1995, with the Soybeans November
futures contract priced at 608.5. First click Calculate,
then select Prices. Then select Grains under the
heading Commodity Option Prices.
The Beginning Date is again today's date. Tab to Expiration
Date and type in the expiration date, which in this case is
October 20, 1995. Again, to select the month, tab to it and just
type in the first letter of the month or use the arrow key.
Now tab to the Futures Price and enter 608.5. Tab to Strike
Price and enter 650. Tab to Volatility and enter the
historical price volatility for the Soybeans futures contract.
(Refer to Chapter 4 to determine volatility.)
Presently, we will use a volatility of 40%, or .40. So enter .40 in the
Volatility entry box. Tab to Interest Rate and enter the
3-month Treasury Bill rate (i.e., .05 for 5%). Then tab out of this box.
Always tab out of an entry box where you have made a change before activating
a calculation. Now you are ready to calculate the theoretical price of
the Soybeans call. Click on Call Prices and check the Message
Center for the results. (See Figure
5)
As you can see, the theoretical Soybean call price is 28
5/8¢, and your probability of profit of 29%, if you buy the
option at its theoretical price and hold until expiration. If you
are an option writer, your probability of profit would be the
inverse of 29%. In other words, 29% subtracted from 100%, giving
you a Probability of Profit of 71% (100 - 29 = 71).
Multiple Futures Options
You can also determine the theoretical price on a whole series
of futures options. Let's use Treasury Bonds to demonstrate this
feature.
We will determine the theoretical price for a series of options on the
September and December Treasury Bond futures contracts. Click on Calculate
in the menu bar. Select Prices, and then select Multiple Futures
Prices. Tab to Expiration Dates and enter the expiration date
for the September Treasury Bond option, and then the December Treasury
Bond option. For our example, the September options expires on August
18, the December options expires on November 18. (See Figure 6)
Now tab to the First Futures Price and enter the
September Treasury Bond futures price for August 4, 1995 -- 110
25/32. You enter this price as 110.25 and it will convert the
decimal to a fraction -- but first click the Bond box
below with your mouse.
Now tab to the Second Futures Price and enter the
December Treasury Bond futures contract price of 110 9/32, or
110.09.
Now tab to Beginning Strike Price and enter the lowest
strike price on which you want to price options. Continue to Ending
Strike Price and by using the arrow key, select the highest
strike price you wish to use.
Strike prices for bonds are in 2-point increments. Therefore,
you must change the increment rate. To do this, click Extras
in the top menu bar. Select Configure. Under the category
of Multiple Strike Price Increment Value, click Custom
and Tab to the entry box and enter the number 2, and click Save.
In Figure 6,
we used a low strike price of 100 and a high strike price of 114. Now
Tab to Volatility and enter a volatility of 8.5%, or .085. Tab
out of Volatility and click Put Prices.
Figure 7
shows the theoretical Put Prices Table generated by this calculation.
By clicking on File, you can either print this table or return
to the program. As you can see, Treasury Bond options are quoted in points
and 64ths.
Other Commodities
When attempting to determine the theoretical value of a
futures option other than a grain or bond -- such as gold,
silver, copper, the currencies, cattle, hogs, oil, etc. -- select
Other Commodities under the Prices menu.
Using Configure
Under the Extras menu in the top menu bar, select the item Configure
(see Figure
8). As we saw when pricing Multiple Futures Options, you can change
the increment value between strike prices -- with stocks the typical increment
is 5 points, but the Option Exchanges are now experimenting with 2 1/2
price increments. So as needed, you can change the increment you will
use. In addition, you can decide to display the Delta, Gamma, Vega and
Theta every time you price an option by selecting Always. You can
also specify the Startup Screen.
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