1.2 Definitions
1.2 Definitions
An option
is a contract between two parties: a
buyer and a seller (or option writer).
The buyer pays the seller a price called the premium, and in
exchange, the option writer gives the buyer the right (but not the
obligation) to buy or sell some underlying security at some pre-specified
price for some pre-specified period of time.
An option to buy is a call option, and an option to sell is a
put option. The pre-specified price
is called the strike or exercise price, and the option's life is called the time
to maturity or time to expiration.
If the right to exercise is "any time until
maturity" then the option is called an American option.
If the right to exercise is only "at the time of maturity" then
the option is referred to as a European option.
The majority of options traded are American options.
All stock options, for example, are American, as are most options on
stock indices, on futures, and on currencies.
Commonly traded European options include those on the S&P 500 index
and on some currencies.
The
specified rights and obligations in an option contract determine the cash flows
from the contract. Consider the
rights and obligations specified by a European call option.
This option can be exercised only at its time of maturity, and the
decision whether to exercise depends upon whether the option finishes
in-the-money or out-of-the-money. An
option is said to be in-the-money or out-of-the-money based upon its current
exercise value.
For
example, assume the possible stock values at the time a European strike 30 call
option expires are 20 and 40. If
you hold one call option, you have the right, but not the obligation, to buy the
stock for 30.
Suppose
the stock value is 20. If you
exercise your option, you are buying the stock for 30, when you could acquire it
in the market for 20. That is, you
would realize a loss of 10 by exercising. In
this case the option is out-of-the-money.
If,
on the other hand, the stock price is 40, it pays you to exercise the option. By exercising, you get to buy the stock for 30 when its
current price is 40. Here your
option is in-the-money.
In
summary, your exercise decision at the end of the life of a European option is
determined by whether the option is in-the-money or out-of-the-money.
The exercise decision for an American option is not this straightforward
and is discussed in greater detail in Chapter 3 (see topics 3.3-3.5, American
Call Option, American
Put Option and Dividends
and American Options.
In
general, if X is the strike price and S
is the value of the stock at the time the option expires, then the payoff C
from a call option is
C
= max{0, S - X}.
This
terminal payoff for a call option is shown in Figure 1.1:
Figure 1.1
Terminal Payoff for a Call Option
The
call is worthless if S < X, but its
value increases linearly with the stock price as long as S
> X. That is, if you own a
call option, you receive cash from exercising if the stock price is greater than
the exercise price. Otherwise, you
do not exercise the option.
Of
course, owning a call requires buying it, so you pay something for it.
Whether you gain from owning a European option at the time of maturity
depends upon two things. First, it
must finish in-the-money and second, the amount by which it finishes
in-the-money must exceed what you paid for it.
Of course, if significant time has elapsed between the time at which you
purchase the option and the time you exercise it, you must also account for
interest lost on the money you used to buy the option.
The
terminal payoff for a put option is:
P
= max{0, X - S}, shown in Figure 1.2 where "terminal" means at
maturity.
Figure 1.2
Terminal Payoff for a Put Option
In
this case, you receive cash from exercising if the price of the stock falls
below the strike price. Otherwise,
you do not exercise the option.
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Financial Trading System