$4.$ 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.

Delaying exercise delays the payment of the strike price. This means that the option holder is

able to earn interest on the strike price for a longer period of time. Delaying exercise also

provides insurance against the stock price falling below the strike price by the expiration

date.