Maximum Value of a Call
A call
option also has a maximum value:
C(S0, T, X)) ≤ SO
The call
is a conduit through which an investor can obtain the stock The most one can
expect to gain from the call is the stock’s value less the exercise price. Even
if the exercise price were zero, no one would pay more for a call than for the
stock. However, one call that is worth the stock price is one with infinite
maturity.
The Value of a Call at Expiration
The price of a call at expiration is given as:
C(ST, 0, X))= Max(0, ST - X).
Because there is no time remaining in the options life, the call price contains no time value. The prospect of future stock price increases is irrelevant to the price of the expiring option, which will be simply its intrinsic value. At expiration, an American option and a European option are identical instruments. Therefore, this rule holds for both types of options.
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