An option buyer will exercise a call or put option at maturity only if it returns a positive payoff—that is:
- (ST − X) > 0 for a call
- (X − ST ) > 0 for a put
If not exercised, the option expires worthless and the option buyer’s loss equals the premium paid.
At any time before maturity (t < T), buyers and sellers often gauge an option’s value by comparing the underlying spot price (St ) with the exercise price (X) to determine the option’s exercise value at time t. This is the option contract’s value if the option were exercisable at time t. The exercise value for a call and a put option at time t incorporating the time value of money is the difference between the spot price (St ) and the present value of the exercise price (PV(X)), as follows:
Call Option Exercise Value:
