Options Pricing: A Beginning

Yahoo! (Nasdaq: YHOO  ) shares sell for $30. You like the company. You like the price. In fact, you really like the price. So much so, that in addition to buying shares outright, you decide to augment your potential gains by buying some call options. If you're right, the price of the shares will rise and take the value of the options with it. But which options should you buy? What strike price? What expiration date? How will the option price behave as the stock price rises? What if the stock price falls? What happens as we approach the expiration date?

Two component pricing
An option price is the sum of two components: intrinsic value (IV) and time value (TV),

Option value = IV + TV

IV is the difference between the stock price and the option's strike price. However, IV cannot be less than zero, since the optionholder wouldn't exercise a call with a strike price of $30 if the same stock is trading in the market at $25. (If you know someone who would do such a thing, please email me their contact information.) IV is calculated based on how the underlying stock price moves in relation to the option strike price:

Stock Price < Strike Price

Stock Price > Strike Price

Stock Price = Strike Price

Call

$0

Stock Price - Strike

$0

Put

Strike Price - Stock Price

$0

$0

TV is simply the premium that people are willing to pay for the potential upside of the stock until expiry. Options can be termed "wasting assets." Over time, as expiration draws near, TV will get smaller and smaller until there's finally no remaining time and TV = 0. Thus, at expiry, the value of the option is simply IV. Prior to expiry, TV is always positive even though it may be very, very small.

Back to reality
Consider the following call options on Yahoo! (recall that Yahoo! currently sells for $30):

Option Number

Strike Price

Symbol

Ask Price

Expiry

IV

TV

1

$27.50

YHQEY

$3.60

May-07

$2.50

$1.10

2

$27.50

YHQGY

$4.30

Jul-07

$2.50

$1.80

3

$27.50

YHQJY

$5.10

Oct-07

$2.50

$2.60

4

$30

YHQEF

$1.95

May-07

$0

$1.95

5

$30

YHQGF

$2.75

Jul-07

$0

$2.75

6

$32.50

YHQGZ

$1.60

Jul-07

$0

$1.60

There are three key observations from this table:

1) Anytime the strike price is greater than or equal to the current stock price, IV is zero. In such cases, the option value is solely attributable to TV, and the expectation (hope?) that the price will get itself up above the strike price by expiration. The interaction between IV and TV is illustrated in the following price curve:

Jul-07 $30 Yahoo! Call

2) The less time remaining until expiry, the lower the TV. (Presumably, this is intuitive.) Note the three options all having $27.50 strike prices, and hence identical IVs. Then note that the May option has only $1.10 of TV, while the October call has $2.60 of TV. More time imparts greater value.

3) For options with a common expiry date, TV is maximized when the strike price and the stock price are equal. As the stock price moves in either direction, TV falls.

These latter two points are illustrated in the following chart. Observe that TV is maximized at the strike price and that the options with less time remaining are seeing their TV decay, and their curves falling to the blue IV line. 

Price Curves for Different Expires

Money-ness
You'll hear phrases like "in-the-money" or "out-of-the-money" bandied about. This is just a fancy way of denoting whether an option has intrinsic value or not. If IV is positive, the option is said to be in-the-money. If IV is zero, it's termed out-of-the-money (pretty complicated, no?)

Expressing options as the sum of IV and TV also leads to the conclusion that early exercise of options generally doesn't make sense (though there are, as always, exceptions to the rule). The thinking goes like this:

1) An option is worth IV + TV.

2) I can exercise it now and receive IV, or

3) I can sell the option and receive IV + TV.

4) IV + TV is more than IV. Therefore, selling an option rather than exercising early is the superior choice.

There is always the potential for option holders to act irrationally and exercise even though they give up TV that they could have harvested by selling the option. Fortunately, such cases are rare. There is, however, a situation where early exercise may become an issue.

Options on dividend-paying stocks
If a company pays a dividend, particularly a hefty one-time dividend, it can provoke early exercise. In theory, a stock's price falls on the ex-dividend date by the amount of the dividend. Option holders don't receive the dividend, though, so they might sell the option before the ex-dividend date to avoid the price drop. 

If, however, the dividend is greater than the remaining TV of an option, then early exercise can make sense.

Consider a stock selling for $41 that is going to pay a $1 dividend, going ex-dividend tomorrow. A call option on the stock has a $30 strike price, sells for $11.50, and expires a week later. This option has an IV of $11 and $0.50 of TV. Assuming that the stock price falls by the amount of the dividend as anticipated (and for ease of calculation, we'll assume the stock price stays flat to expiry), the option holder is better served by exercising early.

Early exercise means that the option holder pays $30 for shares currently worth $41. He then receives a dividend of $1 and continues to hold shares worth $40. Conversely, holding the option through the ex-dividend date until expiry sees the remaining TV dissipate, and the holder ends up with just the shares worth $40. 

Next up: Option pricing seems awfully tied to outside influences. Is there a quick way to see how much I can profit or lose?

Check out more of our options series here.

If you are interested in receiving more information from The Motley Fool about investing in options, please click here.

Fool contributor Jim Gillies owns no shares of any company mentioned. Yahoo! is a Stock Advisor pick. The Fool has a disclosure policy.


Read/Post Comments (5) | Recommend This Article (93)

Comments from our Foolish Readers

Help us keep this a respectfully Foolish area! This is a place for our readers to discuss, debate, and learn more about the Foolish investing topic you read about above. Help us keep it clean and safe. If you believe a comment is abusive or otherwise violates our Fool's Rules, please report it via the Report this Comment Report this Comment icon found on every comment.

  • Report this Comment On January 25, 2009, at 6:09 PM, Fullstep wrote:

    One extremely conservative way to buy stocks is to keep the bulk of your money (say 90%) in t-bills and buy out of the money call options on an underlying index like the S&P 500.

    If the market falls or rises a lot (is very volatile) you will be better off with options. How so? A big rise will be leveraged and you will make more money than from merely owning the stocks.

    A big fall will leave you with 90% of your money plus interest on the t-bills.

    The amount you pay for the options reflects the expected market volatility over the life of the option. How do you know future volatility? You don't. An option buy is a bet on future volatility. If the market moves a lot (either way) you will be better off with the options. If the market moves sideways forever a 100% stock position will have added some dividends and will be better than your alternative 90% t-bill plus interest.

    So, options win on a big move up or down. Stocks win if they move sideways. Of course, options get more expensive when "the market" expects lots of future volatility.

    FInally, the worst advice I ever received was from a broker (in 1974) who advised me to sell calls against my stock position to generate some extra income. This is an extremely risky thing to do. It is sort of the opposite of the t-bill long call strategy I described above. If you sell calls and the stock moves up substantially you limit your gains. On the other hand, if the stock moves down quickly you have almost all of your money (minus the premium you got for selling the option) at risk.

    Only sell options on a stock you expect to move sideways! Of course, sideways stocks are not very volatile and you will not get much in the way of a premium for taking the downside risk of owning the stock.

    Another way to describe buying a stock and selling a call against it is "covered writing of a call." This is equivalent to "naked put selling". If your broker called you and suggested that you try "naked put selling" I doubt you would do it...

  • Report this Comment On August 23, 2009, at 9:50 PM, AirForceFool wrote:

    If you really knew a stock was going to go down you would sell of course, and selling calls against would be a bad idea... but if you were holding a stock for the long haul, and would be happy selling at a particular price, selling calls is a good idea... of course you have to be willing to let the shares go for x% gain... and if the stock does tank, you simply buy the call back cheap, and are actually better off then if you hadn't sold the calls in the first place...

    Chris

    just my two cents, since I like selling calls.... to each his/her own of course.

  • Report this Comment On April 19, 2010, at 10:07 PM, Mstinterestinman wrote:

    I made a little extra income selling callsit all depends on how volatole the stock you hold is.

  • Report this Comment On April 15, 2011, at 10:09 PM, UFOFred wrote:

    I found your 2007 article on options to be useful. But you have a bit of an error in your example "Jul-07 $30 Yahoo Call". The red line, labeled Time Value is actually Intrinsic Value plus Time Value. The time value is the area between the blue and red curves.

    I modified your graphic for use in a presentation for my investment club. Besides correcting the label for the red curve, I shaded the TM area and labeled the in- and out of the money area.

    If you would like the modified graphic as a gif file, let me know. I presume you can get my email address from Fool archives.

    Fred

  • Report this Comment On April 15, 2011, at 10:10 PM, UFOFred wrote:

    Correction to above comment: TM should be TV (time value).

    Oops.

    Fred

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