The Mathematics of Financial Modelingand Investment Management

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2-Financial Markets Page 67 Wednesday, February 4, 2004 1:15 PM


Overview of Financial Markets, Financial Assets, and Market Participants 67

option is $100 and the current asset price is $105, the intrinsic value is
$5. That is, an option buyer exercising the option and simultaneously
selling the underlying asset would realize $105 from the sale of the
asset, which would be covered by acquiring the asset from the option
writer for $100, thereby netting a $5 gain.
When an option has intrinsic value, it is said to be “in the money.”
When the strike price of a call option exceeds the current asset price, the
call option is said to be “out of the money”; it has no intrinsic value. An
option for which the strike price is equal to the current asset price is
said to be “at the money.” Both at-the-money and out-of-the-money
options have an intrinsic value of zero because it is not profitable to
exercise the option. Our call option with a strike price of $100 would
be: (1) in the money when the current asset price is greater than $100;
(2) out of the money when the current asset price is less than $100; and
(3) at the money when the current asset price is equal to $100.
For a put option, the intrinsic value is equal to the amount by which
the current asset price is below the strike price. For example, if the strike
price of a put option is $100 and the current asset price is $92, the intrin-
sic value is $8. That is, the buyer of the put option who exercises the put
option and simultaneously sells the underlying asset will net $8 by exer-
cising. The asset will be sold to the writer for $100 and purchased in the
market for $92. For our put option with a strike price of $100, the option
would be: (1) in the money when the asset price is less than $100; (2) out
of the money when the current asset price exceeds the strike price; and (3)
at the money when the strike price is equal to the asset’s price.
The time premium of an option is the amount by which the option
price exceeds its intrinsic value. The option buyer hopes that, at some
time prior to expiration, changes in the market price of the underlying
asset will increase the value of the rights conveyed by the option. For
this prospect, the option buyer is willing to pay a premium above the
intrinsic value. For example, if the price of a call option with a strike
price of $100 is $9 when the current asset price is $105, the time pre-
mium of this option is $4 ($9 minus its intrinsic value of $5). Had the
current asset price been $90 instead of $105, then the time premium of
this option would be the entire $9 because the option has no intrinsic
value. Clearly, other things being equal, the time premium of an option
will increase with the amount of time remaining to expiration.
There are two ways in which an option buyer may realize the value
of a position taken in the option. First is to exercise the option. The sec-
ond is by selling the call option for $9. In the first example above, sell-
ing the call is preferable because the exercise of an option will realize a
gain of only $5—it will cause the immediate loss of any time premium.
There are circumstances under which an option may be exercised prior
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