price ofthe underlying security. Here, we refer to the intrinsic value ofan
option, which corresponds to the amount that an option is said to be ITM.
(Note that only ITM options have intrinsic value. Fortunately, we do not
need any computer programs to calculate intrinsic value; rather, we only
need a simple subtraction formula.) Figure 4-2 illustrates the formula
used to determine the intrinsic value of an in-the-money option.
As we can see, then, the intrinsic value of an ITM depends upon the
relationship of the option's strike to the current price of the underlying
securit~ Because the option's strike price is a constant, the intrinsic value
of an option will fluctuate dollar for dollar with any price change of the
underlying security (as long as the option remains ITM). As soon as the
price ofthe underlying security moves below a call option's strike price or
above a put option's strike price, that option would become ATM or OTM
and would have no intrinsic value. To summarize:
1. The intrinsic value ofan option is the amount that an option is ITM.
2. OTM and ATM options have no intrinsic value.
Extrinsic Value
Although intrinsic value plays a fundamental role in determining the
price of an option, it alone is not responsible for the overall pricing of the
option. In fact, intrinsic value is only one component of the price of an
option. Stock options have both intrinsic and extrinsic value. The price of
an option is the sum of its intrinsic aDd extrinsic values.
The extrinsic value of an option is that part of its price that is determined
by certain variables other than the price ofthe underlying security
and the strike price. These variables are as follows:
1. Time to expiration
2. Interest rates
3. Volatility
4. Dividends of the underlying security (if applicable)
We will examine the impact of each of these variables on option pricing
separately: First, however, let's look at the simple formula for identifying
extrinsic value. Figure 4-3 is an example of the formula used to
determine the extrinsic value of an option.
Before proceeding, we should give you a few words about terminology:
In the industry, extrinsic value is frequently referred to in a number of
ways (such as time value, time premium, or premium value). Informally,
this concept is often referred to as the juice or fluff ofthe option. From this
point forward, we will use the term time premium interchangeably with
extrinsic value. But although we are using the word time premium, we
should keep in mind that extrinsic value is influenced by more than just
time until expiration. To complicate matters a bit more, an option's overall
(or total) price-its intrinsic and extrinsic values combined-is frequently
referred to in the industry as the option's premium. In this book,
when we refer to an option's premium, we are speaking about the overall
price of the option. When we talk about the time premium, on the other
hand, we refer to the extrinsic value of a particular option.
Having reviewed these basic formulas, we can now gain some insight
as to how the time to expiration, interest rates, and volatility impact the
price of an option. In the following example, consider how differing input
variables will affect the price outcome for options that are listed for two
different stocks.
Assume the following:
1. Stocks ABC and XYZ are both trading at $52.
2. ABC is an Internet company:
3. XYZ is a well-established, traditional retailer.
4. April options have 30 days until expiration.
5. May options have 58 days until expiration.
6. You are interested in purchasing stock in both ABC and XYZ.
Consider the role of interest rates and the time to expiration when
comparing the purchase of April 40 calls on both ABC and XYZ to buyingstock:
1. By buying the stock, you pay $52 per share now. Ifyou purchase the
April 40 call, you defer payment of the $40 per share exercise price
until you exercise the option. In the meantime, you can invest this
$40 per share and earn interest. The amount of interest earned
depends on the time until exercise and the interest rate that you will
be paid on the funds. This economic benefit has a value that will be
reflected in the price of the option. We need to make two important
observations here:
a. Benefit is the same for ABC and XYZ. This benefit is measured
solely by the amount of money involved ($40 per share in this
case), the interest rate, and the time until expiration. Therefore,
the benefit would be the same whether you were considering an
investment inABC or XYZ.
b. The more time until exercise, the larger the economic benefit.
You could earn more interest-in fact, approximately twice the
amount-by delaying exercise until May: Thus, the price of the
May 40 calls will include a larger fee for the right to earn interest
by investing the amount needed to exercise the calls until
option exercise.
2. In this example, consider the role ofvolatility and time to expiration:
a. If the stock plunges to $30 prior to April expiration (the anticipated
time that you would exercise your call), you would lose $22
per share if the stock were purchased (but only the price of the
call ifyou acquired that instead). This reduction in your risk has
a value that will also be reflected in the price ofthe option.
b. The benefit is different for ABC and XYZ. You would probably
assess that the risk of this significant price move prior to April
expiration is greater for ABC than for XYZ and would therefore
be willing to pay more for this risk protection in the case ofABC
than XYZ. Surely the seller of the April 40 calls would charge
more for assuming this risk of a large move in the price of the
stock prior to April option expiration in the case ofABC than for
XYZ. For this reason, the price ofthe ABC April 40 call will likely
be greater than the price of the XYZ April 40 call.
c. The more time until exercise, the greater the risk to the seller.
For the same, obvious reason that the premium on a 60-day
health insurance policy for an individual is greater than the premium
on the same policy for the same individual if the term is
only 30 days, the price of the May 40 calls in ABC will include a
larger amount that is attributable to the risk that the stock price
will move away from $40 by May expiration than the Apr 40 calls
by April expiration.
Without attempting to calculate the fair value of the benefits offered
by the April 40 calls over the immediate purchase of the stock, it should
now be clear that the factors of time, interest rate, and anticipated stock
price volatility all impact the price of an option. We will now turn our
attention to methods that are available for quantifying the value ofthese
and other factors in order to address the question posed at the beginning
of this chapter: "How can I tell if an option is fairly priced?"
Read More: Factors Affecting the Price of an Option
