"The Ups & Downs of Options Prices" by J. Bittman, Options Institute
cnbc.com
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Edited:
>>>"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 options prices change. Understanding some of the reasons options prices behave the way they do 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: The price of XYZ stock is 50; it is 90 days until option expiration; and the price of the XYZ 90-day, 50-strike call is 3 1/4. 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 3 1/4.
b. The call price will rise by 1/4 to 3 1/2.
c. The call price will rise by 1/2 to 3 3/4.
d. The call price will rise by 1 to 4 1/4.
Question 2:
The beginning assumptions are the same: The price of XYZ stock is 50; it is 90 days until option expiration; and the price of the XYZ 90-day, 50-strike call is 3 1/4. 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 1/2 to 2 3/4.
b. The call price will decrease by 1 to 2 1/4.
c. The call price will decrease by 1 1/2 to 1 3/4.
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 4 percent, no dividends and volatility of 30 percent.
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*** Table 1 in the link above
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The Answers
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 "3 3/4," so the answer to Question 1 is "C. The call price will rise by 1/2 to 3 3/4."
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 "2 1/4," so the answer to Question 2 is "B." The call price will decrease by 1 to 2 1/4."
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 3 1/4 to 3 3/4), so this call would be described as having a delta of "0.50."
Generally speaking, when an option is at-the-money – the stock price equals the strike price -- its delta is about 0.50. Options that are out-of-the-money – the strike price is 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 deltas 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 don’t decrease at the same rate as time passes to expiration. In this case, for example, the time to expiration decreased by 50 percent from 90 days to 45 days. The price of the 50 Call, however, decreased by about 31 percent to 2 1/4 from 3 1/4.
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 vs. Trading Stocks
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 two days of the report might lead to trading a different option than a forecast for a stock price move within two 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 a 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. From time to time, however, they may have more open positions than stock traders.
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 Chicago Board Options Exchange’s Web site (http://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 options-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 options price behavior. The next step will be applying what you learn to your actual trading decisions.
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James B. Bittman is a senior instructor at the Options Institute, the educational arm of the Chicago Board Options Exchange. He is also the author of Options for the Stock Investor.
Options involve risks and aren’t suitable for everyone. Prior to buying or selling an option, an investor must receive a copy of Characteristics and Risks of Standardized Options, which may be obtained from your broker or from the Chicago Board Options Exchange at 400 S. LaSalle, Chicago, Ill., 60605. Investors considering options should consult their tax adviser as to how taxes may affect the outcome of contemplated options transactions. <<< |
