# The Ups and Downs of Option Prices

&#8220;The stock went up, but my call didn&#8217;t!&#8221; &#8220;My call doubled when the stock rose only \$2!&#8221; Some of the most commonly expressed frustrations with options are about how option prices change. This article will explain some of the reasons why option prices behave the way they do. Understanding these concepts may help you be a better options trader. Let&#8217;s begin with a two-question test. Carefully read the

“The stock went up, but my call didn’t!”

“My call doubled when the stock rose only \$2!”

Some of the most commonly expressed frustrations with options are about how option prices change. This article will explain some of the reasons why option prices behave the way they do. Understanding these concepts may help you be a better options trader.

Let’s begin with a two-question test. Carefully read the beginning assumptions before choosing an answer.

Question 1: There are three assumptions:

1. The price of XYZ stock is \$50.

2. It is 90 days to option expiration.

3. The price of the XYZ 90-day, 50-strike call is 3¼.

Question: What do you expect the price of this call to be if the stock price rises to \$51 today? (For the sake of simplicity, assume no change in time to expiration.)

Choose one:
a. The call price will remain unchanged at 3¼.
b. The call price will rise by ¼ to 3½.
c. The call price will rise by ½ to 3¾.
d. The call price will rise by 1 to 4¼.

Question 2: The beginning assumptions are the same:

1. The price of XYZ stock is \$50.

2. It is 90 days to option expiration.

3. The price of the XYZ 90-day, 50-strike call is 3¼.

Question: What do you expect the price of this call to be if the stock price remains unchanged (at \$50) for 45 days and other factors such as interest rates, dividends and volatility remain the same?

Choose one:
a. The call price will decrease by ½ to 2¾.
b. The call price will decrease by 1 to 2 ¼.
c. The call price will decrease by 1½ to 1¾.
d. The call price will decrease by 1 5/8 to 1 5/8.

For the answers, look at Table 1 which presents theoretical values of a \$50 Call at different stock prices and different days to expiration assuming interest rates of 5%, no dividends and volatility of 30%.

Table 1
\$50 Call - Theoretical Values
(At Various Stock Prices and Days to Expiration)
Volatility – 30%; Interest Rates 4%; No Dividends

 Stock Price 90 Days 75 Days 60 Days 45 Days 30 Days 15 Days EXP 55 6 5/8 6 3/8 6 5 3/4 5 1/2 5 1/8 5 54 5 7/8 5 1/2 5 1/4 5 4 5/8 4 1/4 4 53 5 1/8 4 3/4 4 1/2 4 1/8 3 3/4 3 3/8 3 52 4 3/8 4 1/8 3 3/4 3 3/8 3 2 9/16 2 51 3 3/4 3 1/2 3 1/8 2 3/4 2 3/8 1 3/4 1 50 3 1/4 2 7/8 2 5/8 2 1/4 1 13/16 1 1/4 0 49 2 3/4 2 3/8 2 1/8 1 3/4 1 5/16 3/4 0 48 2 1/4 1 7/8 1 5/8 1 1/4 7/8 1/2 0 47 1 3/4 1 1/2 1 1/4 1 5/8 1/4 0 46 1 3/8 1 1/8 7/8 5/8 3/8 1/8 0 45 1 1/8 7/8 5/8 1/2 1/4 1/16 0

Note: The prices in this table are presented for illustration purposes only. They do not represent any actual option prices and are not intended to. Option prices on real stocks will differ significantly from those presented here.

Each of the rows in Table 1 is a different stock price, and each of the columns is a different number days to expiration. For example, the cell in Table 1 which contains a 50 Call price of 3¼ and the starting assumptions for the questions is the cell in the middle row (stock price of 50) and the left-most column (90 days).

To find the answer to Question 1, simply go up one cell in the same column (stock price 51, 90 days). The indicated call value is “3¾,” so the answer to Question 1 is “c. The call price will rise by ½ to 3¾.”

To find the answer to Question 2, simply move three cells to the right in the same row (stock price 50, 45 days). The indicated call value is “2¼,” so the answer to Question 2 is “b. The call price will decrease by 1 to 2¼.”

The Concept of Delta

The important concept from Question 1 is that, for a \$1 change in the underlying stock price, the call option value will almost always change by less than \$1. The term “delta” is used to describe the expected change in an option’s price for a \$1 change in the underlying stock’s price. In this case, the stock price rose by \$1 (from \$50 to \$51) and the 50 Call rose by 50 cents (from 3¼ to 3¾), so this call would be described as having a delta of “0.50.”

Generally speaking, when an option is at-the-money (stock price equals strike price), its delta is approximately 0.50. Options that are out-of-the-money (strike price above the stock price for calls and below the stock price for puts) have deltas less than 0.50. And options that are in-the-money have delta’s that are greater than 0.50. Calls have deltas that are positive, i.e., +0.50, and puts have deltas that are negative, i.e., -0.50.

Non-Linear Time Decay

The important concept from Question 2 is that, assuming factors other than time to expiration remain constant, option prices do not decrease at the same rate as time passes to expiration. In this case, for example, the time to expiration decreased by 50% from 90 days to 45 days. The price of the 50 Call, however, decreased by approximately 31% from 3¼ to 2¼.

Looking across any row in Table 1, you will observe that the decrease in option value from the passage of time, so-called “time erosion,” varies depending on whether an option is in-the-money, at-the-money or out-of-the-money. But, for practical purposes, all options decay with the passage of time, so option traders should consider this when making trading decisions.

Trading options is different than trading stocks for a number of reasons. First, options have an expiration date and are affected by time erosion. This means that traders should include a time forecast as part of their complete market forecast. Although this may sound difficult, a little practice may change your mind. Consider, for example, a trading decision made prior to an earnings report. A forecast for a stock price move within 2 days of the report might lead to trading a different option than a forecast for a stock price move within 2 weeks.

Second, because different options have different deltas, option traders must be more specific in their stock price forecasts. A forecast of a smaller stock price change might lead to the selection of an at-the-money or in-the-money option, while a forecast for a larger price change might lead to the selection of an out-of-the-money option.

Third, option traders should manage their capital differently than stock traders. The decision to purchase 200 shares of a stock trading at \$50 per share, is very different that the decision to purchase 100 call options trading at \$1 each, even though both trades involve an investment of \$10,000, not including commissions. Typically, option traders will devote a smaller portion of total capital to each trade, however, even with this smaller amount of capital committed, the risk of loss can be greater due to time decay. From time to time, however, they may have more open positions than stock traders.

Finally, unlike stock owners, options traders to not receive dividends paid on the underlying stock, nor do they receive voting rights.

Developing Realistic Expectations

Mastering the concepts in Table 1 – delta and time decay – is an important step toward the goal of developing realistic expectations about how option prices might and might not change. Tables similar to Table 1 can be created using any standard option pricing software. Table 1 was created using The Options Toolbox, a program which can be downloaded free of charge from the web site of The Chicago Board Options Exchange (www.cboe.com).

Creating “practice problems” is also a good way to study how option prices change. Start by choosing a hypothetical stock price, a strike price, a number of days to expiration a dividend rate and a volatility percentage. Enter these variables into an option pricing computer program, and ask yourself something like the following: “What do I estimate the option price will be if the stock price rises \$5 in two weeks?” You can then use the software to get an estimate. After several exercises of this nature, you will have a better understanding of option price behavior. The next step will be applying what you learn to your actual trading decisions.

FOR REGISTERED REPRESENTATIVES ONLY. NOT FOR CUSTOMER DISTRIBUTION.

Options are not suitable for every investor. For more information, consult your investment advisor. Prior to buying and selling options, a person must receive a copy of Characteristics and Risks of Standardized Options which is available from your broker or from The Options Clearing Corporation (OCC) by calling 1-888-OPTIONS, or by writing to OCC at One North Wacker Dr. Suite 500, Chicago, IL 60606.

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