### CFA Practice Question

A put has an exercise price of \$75 with an expiration period of 75 days (360-day year basis); the risk-free rate is 3.5%. Which of the following statements is correct?
A. The put has a minimum value of \$0 and a maximum value of \$74.46 if it is an American put
B. The put has a minimum value of \$0 and a maximum value of \$74.46 if it is a European put.
C. The put has a minimum payoff of \$65 at expiration regardless of whether it is American or European.
Explanation: Since a European put cannot be exercised before expiration, its maximum value is limited by the present value of the exercise price, should the stock drop to zero. Thus, the maximum value of a European put <= 75/(1.035)(75/360) = \$74.46.

The minimum value is zero since the put remains unexercised if the stock price goes up instead of down.

### User Contributed Comments3

User Comment
GBolt93 why would the american put have different min and max values? Even if you can exercise an american put at any time I don't see how it could be worth more than the PV of the difference between it's exercise price and 0
Lambo83 For American puts:

P = max(0, X - So)
As it can exercised at anytime you don't discount the exercise price to the present value. Hence the max price for the American put will be \$75.
KosyoAr @Lambo83 I think you meant value there... Option prices are set at the beginning and do not flactuate
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