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Software for Pricing Options
by Kenneth R. Trester
and Robert P. Swanson
Chapter 4 - The Name of the Game is Volatility
The most important component in measuring the fair price for a
stock, index or futures option is the price volatility of the
underlying stock, index or future. In other words, the average
amount the stock, index or futures price fluctuates up or down in
a given time. Your measure of the underlying price volatility
will be your determinant of how successfully you are able to
measure the fair price for an option.
What you are trying to do is estimate the future volatility of
the underlying stock, index or futures. You do this by
determining the historical volatility of the underlying
instrument. Historical volatility is defined as a standard
deviation of a change in price as used in pricing models such as
OPTION MASTER®.
There are several published sources where you can get the
historical volatility for stocks, indexes and futures. For
example, the historical volatility for almost 200 stocks are
published in the Trester Complete Option Report,
available from The Institute for Options Research, Inc., P.O. Box
6586, Lake Tahoe, Nevada 89449. Historical volatility for most
option stocks, indexes and currencies are published in Daily
Graphs Option Guide, P.O. Box 66919, Los Angeles,
California 90066.
OPTION MASTER® will also calculate any historical volatility that you
desire. Typical historical volatility ranges for stocks, indexes and futures
contracts are presented in Table I.
To calculate historical volatility, click on Calculate
in the top menu bar, then select Volatility and then
select Historical Volatility. Now you are in the Calculate
Volatility screen.
To measure historical volatility, you need to enter past
prices for the underlying stock, index or futures.
A quick and dirty way to calculate a historical volatility
would be to enter the high and low price for the past year for a
stock, index or commodity. But this historical volatility figure
is crude and may be inaccurate. In fact, the more time you spend
in measuring volatility, the more successful and accurate you
will be in determining the true theoretical value for the options
that you are reviewing.
To measure historical volatility, you first select the
observation period by clicking on Day, Week, Month or Year.
Market makers use a daily observation period using prices for
each trading day. Usually, they are a 20 to 30-day history. One
of the reasons that they use this period is because they hold
option positions for very short periods of time. If you plan to
hold an option position for a longer period of time, you should
use a longer price history.
In our research, we found that a 20-week history with one
observation period per week (the closing price on one day each
week) showed a high correlation with the future volatility of the
underlying stock, index or commodity.
Some Practice Sessions
Let's go through two examples to show you how to calculate
historical volatility. The menu screen has been designed for ease
of use, so you may quickly enter prices.
Let's say you wish to calculate the historical volatility for
Microsoft. First, click on Week. The easiest way to enter
data is by using a chart book with a chart of Microsoft, but old
newspapers will also do the job. Select the Microsoft closing
price for one day each week, starting with the earliest week. Try
to be consistent using the same day each week. For example, we
collected the past 10 weeks of price listings for Microsoft, one
closing price per week. We started with 89 ten weeks ago, then
85, 84, 85, 91, 90, 92, 100, 95 and then 92. As you will notice,
we dropped the fractions to allow for faster and easier entry.
Adding the fractions will probably not add much to your accuracy.
Now begin entering these prices in the entry box, Stock or
Futures Price. Hit the Enter or Return key
after each entry.
Now click on Calculate Volatility. As you can see, the volatility
is .311 (31.1%). (See Figure
10) You can calculate volatility at any time during the entry process
as long as you have two entries or more. Now you can save this file by
clicking on the File menu. Make sure that the files you save have
the extension .OMV, so that they will be easy to retrieve.
As you continue to update this file, you can delete previous
prices (i.e., beyond 20 weeks) by clicking the Delete
button after selecting the price you wish to delete. You also can
insert prices by clicking on the stock price after the one you
wish to insert and then clicking the Insert button. Make
sure you have typed in a price before clicking the Insert
button.
Now let's calculate the volatility for a soybeans futures
contract. Again, we will use a 10-week price history Đ one
observation per week. One easy way to get the price history for
futures contracts is to use the Investor's Business Daily.
This newspaper gives good charts of a several months price
history for most futures contracts. In addition, if you have a
good commodity broker, he may have the historical volatility
figures you desire. But make sure the time span for these
volatility figures is long enough to meet your needs.
Here is an example of 10 past weeks of Soybeans Nov. 95 future contract
prices (one observation per week) starting with the earliest prices; they
include $6.21, $6.01, $5.91, $6.27, $5.97, $6.16, $6.31, $6.39, $6.14
and $5.97. Enter these numbers in the Stock or Futures Price entry
box, again hitting the Enter key each time. Now click on Calculate
Volatility. As you can see, we entered the price as whole numbers
to speed up the entry process. (Refer to Figure
11)
Here the volatility is .253 (25.3%). Again, you can save these
prices as a file and later retrieve these prices, delete previous
prices and add new prices to update your volatility. If you are
following a group of different commodities or financial futures,
you can easily and quickly update these volatilities on a weekly
basis much faster and far less expensively than trying to
download prices every day.
Using Implied Volatility
The Windows, DOS and Newton versions of OPTION MASTER®
calculate implied volatility. Implied Volatility is the
volatility determined by the market. It is the volatility built
into the option price so if a silver call option is priced at
10¢ on the exchange, you could use OPTION MASTER® to measure
this option and keep changing the volatility in the pricing
module of the program until the theoretical price was 10¢. That
volatility would be the implied volatility. This implied
volatility is what the market thinks the volatility should be.
Many investors confuse implied volatility with historical
volatility. Implied volatility should not be used in the Pricing
module of OPTION MASTER®, for if you use it for a specific
option, the theoretical price generated would always be the same
as the market price. Never would an option be over or
underpriced.
Implied volatility is quite useful in comparing the options on
the same stock, index or futures contract. If some of the
out-of-the-money calls on pork bellies had a higher implied
volatility than the at-the-money calls, then these
out-of-the-money calls would be overpriced compared to the calls
where the pork bellies price was closer to the strike price.
Another way to use implied volatility is to plot it over a
period of time. Then when the implied volatility is low for a
specific stock, index, or commodity, the options tend to be
underpriced and vice versa.
Implied volatility can also be used with "what if?"
analysis. For example, if you wanted to know what the price of an
IBM Sept 120 call would be worth in two weeks, if IBM moved up to
118, you could change the Beginning Date to two weeks from
now, change the stock price to 118 in the Single Option Price
module of OPTION MASTER® and use the present implied volatility
of the IBM Sept 120 call. Then you would get a good estimate of
the price the IBM Sept 120 if IBM hit 118 in two weeks.
A Practice Session
Let's calculate an implied volatility for the Copper Dec. 120
put priced at 2.35¢ with December Copper priced at 132.40 on
August 4, 1995. This option expires on November 27. Go to the Volatility
module of the program and select Futures Options under the
heading, "Implied Volatility."
Enter the beginning date and expiration date as you did when pricing
options. Then enter the futures price and strike price. Tab to the Option
Price entry box and enter the closing price (settlement price) for
the Copper Dec. 120 put (i.e., 2.35). Click Put Prices and an implied
volatility of .242 (24.2%) is calculated. (Refer to Figure
12)
Now let's calculate the implied volatility on a S & P 100
Index (OEX) Aug 545 call priced at 5/8 when the OEX is priced at
529.60 on August 4, 1995.
First click on Calculate, select Volatility,
then select Stock and Index Options.
Then enter the beginning date and the expiration month of August and
then enter the index price (529.60) and strike price (545). Now Tab to
the option price entry box and enter the closing option price for the
Aug. 545 call of 5/8. Click on Call Prices, and as you can see,
the implied volatility is .11 (11%). (Refer to Figure
13)
A final point to remember: implied volatility is based
on the market price of a specific option. It is the volatility
implied in the option price. Historical volatility is
based on the past price volatility of the underlying stock, index
or futures.
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