CFA Practice Question
Which of the following must be true according to the no-arbitrage principle?
II. An American option must cost at least as much as a European option.
III. A call option must cost no more than the underlying stock.
I. An American stock option must cost at least as much as its intrinsic value.
II. An American option must cost at least as much as a European option.
III. A call option must cost no more than the underlying stock.
A. I and II.
B. I and III.
C. I, II and III.
Explanation: If any of the conditions listed in answers A, B, or C were not true, arbitrage would be possible. If the option costs less than its intrinsic value, the arbitrage would be to buy the option and immediately exercise it and then sell the underlying stock. If a European option cost more than a corresponding American option, the arbitrage would be to write the European option and buy the American option, and then hold both until expiration. If an option costs more than the underlying stock, the arbitrage would be to buy the stock and write the option.
User Contributed Comments 4
| User | Comment |
|---|---|
| Sheikh | You can not always "immediately" exercise the option, recall European options for example ;) 1 would not be true for European options: European put "in the money" can very well be below the intrinsic value |
| lwang014 | however, the put-call parity is specifically to an Eurepean option. |
| lonepine | is this specific to something in the money? i would think out of the money options ... |
| Benloper | I thought the same thing Sheikh - one could need to be able to purchase or sell a security in the future - buy a european option - and be willing to pay more for the stock to have that option.... |