Give two reasons that the early exercise of an American call option on a non-dividend-paying stock is not optimal. The first reason should involve the time value of money. The second reason should apply even if interest rates are zero.
1) Time Value of Money: The early exercise of an American call option on a non-dividend-paying stock is not optimal because of the time value of money. By exercising the option early, the option holder gives up the opportunity to earn interest or returns on the funds that could have been invested elsewhere. Since the option has a finite lifespan, by waiting until the expiration date, the option holder can continue to hold and potentially benefit from any increase in the stock price, while also earning interest on their capital during this period.
2) Opportunity for Future Price Movement: Even if interest rates are zero, early exercise of an American call option on a non-dividend-paying stock is still not optimal because it eliminates the potential for future price movement. By exercising the option early, the option holder loses the opportunity to continue benefiting from any potential increase in the stock price beyond the exercise price. Since the option holder has the right to buy the underlying stock at a predetermined price, waiting until the expiration date allows them to take advantage of any potential positive price movements during the remaining lifespan of the option. Early exercise prevents the option holder from potentially capturing greater profits if the stock price continues to rise.
Reason 1: Time Value of Money
The primary reason that early exercise of an American call option on a non-dividend-paying stock is not optimal is because of the time value of money. By exercising the option early, the option holder would be giving up the opportunity to earn interest or utilize the money in other investments. Since the option holder pays the exercise price upfront upon exercising the option, they would be forgoing any potential gains that could be earned by delaying the exercise and continuing to hold the option.
Reason 2: Opportunity Cost
Even if interest rates are zero, there is still an opportunity cost associated with early exercise. By exercising the option early, the option holder would miss out on any potential future increase in the stock price. Since American call options allow the holder to exercise and buy the underlying stock at a predetermined price (the strike price), it would be more advantageous to delay exercise until just prior to the option's expiration date, especially if there is a possibility of the stock price increasing further during that time period. By holding the option instead of exercising early, the option holder retains the right to benefit from any future price appreciation of the stock.