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Option Master Chapter 4
Download the Option Master Manual - PDF 187k

 

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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