Question

Which of the following statements is false?

A	Put options increase in value as the stock price falls.
B	If two call options have different strike prices but are otherwise identical, the call option with the higher strike price has a lower value than the call option with a lower strike price.
C	A put option cannot be worth more than its strike price.
D	An American option with an earlier exercise date cannot be worth more than an otherwise identical American option with a later exercise date.
E	A put option has a negative intrinsic value when the stock price is higher than the strike price.

Answer 1

D is false.

It is possible that an american option with an earlier exercise date can be worth more than an otherwise identical American option with a later exercise date in the following scenarios:-

Non-dividend paying American Put option. Suppose that the strike price is $10 on the exercise date and the stock price is near zero. By exercising the put immediately, the investor makes a profit of $10.Whereas if the investor waits till a later exercise date, the stock price may increase and the said $10 profit is reduced.

Dividend paying American option. A dividend is assumed to occur at the time of its ex-dividend date. In case the dividends are expected, we can no longer say that an American Option will not be exercised early. Sometimes it is optimal to exercise the call option immediately prior to an ex-dividend date. It is never optimal to exercise a call at other times. The dividend makes up for the early payment of the strike price before the expiration date.