Let's say that a stock's 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 fictional call options on our fictional company.

Option Number

Strike Price

Symbol

Ask Price

Expiry

IV

TV

1

$27.50

[five letters]

$3.60

May-07

$2.50

$1.10

2

$27.50

[five letters]

$4.30

Jul-07

$2.50

$1.80

3

$27.50

[five letters]

$5.10

Oct-07

$2.50

$2.60

4

$30

[five letters]

$1.95

May-07

$0

$1.95

5

$30

[five letters]

$2.75

Jul-07

$0

$2.75

6

$32.50

[five letters]

$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.

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. 

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.

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