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.

Answer 1

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.