16.Shigeo Kishiro recently purchased an American put option and Lendon Grey recently wrote an American call option on the same underlying stock, Tackel Sports (currently trading at $40 per share). Kishiro paid $2.75 for an exercise price of $38.00 and Grey received $3.75 for a strike price of $42. Assume that there are no transaction costs to exercise.

At a stock price of $43:

A)   if Grey exercises, he will have gained a total of $4.75.

B)   the intrinsic put value is $0 and the put is at-the-money.

C)   the intrinsic call value is $1.

D)   the counter-party to Kishiro breaks even.

17.Which of the following statements about the investors is FALSE?

A)   Grey's loss is unlimited.

B)   Grey's gain is limited to the premium.

C)   Grey's maximum gain and Kishiro's maximum loss sum to zero.

D)   Kishiro's gain is limited to the strike price minus the premium.

18.An investor writes a July 20 call on a stock trading at 23 for premium of $4. The breakeven price on the trade and the maximum gain on the trade are, respectively:

A)                                        $24 $4

B)                                        $24 $3

C)                                        $27 unlimited

D)                                        $27 $4

19.An investor bought a 40 put on a stock trading at 43 for a premium of $1. What is the maximum gain on the put and the value of the put at expiration if the stock price is $41?

A)                                        $39 $0

B)                                        $40 $2

C)                                        unlimited       $1

D)                                        $42 $2

20.An investor bought a 15 call for $14 on a stock trading at $20. If the stock is trading at $24 at option expiration, what is the profit and the value of the call at option expiration?

A)                                        -$5 $5

B)                                        $4  -$5

C)                                        -$5 $9

D)                                        $1  $9

答案和详解如下：

16.Shigeo Kishiro recently purchased an American put option and Lendon Grey recently wrote an American call option on the same underlying stock, Tackel Sports (currently trading at $40 per share). Kishiro paid $2.75 for an exercise price of $38.00 and Grey received $3.75 for a strike price of $42. Assume that there are no transaction costs to exercise.

At a stock price of $43:

A)   if Grey exercises, he will have gained a total of $4.75.

B)   the intrinsic put value is $0 and the put is at-the-money.

C)   the intrinsic call value is $1.

D)   the counter-party to Kishiro breaks even.

The correct answer was C)    

The intrinsic value of a call is given as: max [0, S – X], where S = stock price and X = strike price. Here, max [0, 43 – 42] = max [0, 1] = 1.

The other answers are incorrect. The counterparty to Kishiro is the put writer. At a stock price of $43, Kishiro will not exercise (the put is out-of-the money), so the writer has a gain equal to the premium, or $2.75. Grey wrote the option and thus cannot exercise. The intrinsic value of the put is correct at $0, or max[0, X – S], but as previously noted, the put is out-of-the money at a stock price of $43. The put is at-the-money when the stock price is equal to the strike price, or $38.

17.Which of the following statements about the investors is FALSE?

A)   Grey's loss is unlimited.

B)   Grey's gain is limited to the premium.

C)   Grey's maximum gain and Kishiro's maximum loss sum to zero.

D)   Kishiro's gain is limited to the strike price minus the premium.

The correct answer was C)

Although options are a zero-sum game, it is the counterparty exposures that nets to zero. For example, the put buyer’s maximum loss = put writer’s maximum gain = the premium. The other statements are true. Note that the reason why Grey’s loss is unlimited is that he does not currently own the stock. In other words, he has a naked position. If the stock were to rise, Grey would be forced to buy the stock in the open market to settle the exercise of the option. Because the potential for the stock to rise is unlimited, the potential loss for the naked call writer is also unlimited.

18.An investor writes a July 20 call on a stock trading at 23 for premium of $4. The breakeven price on the trade and the maximum gain on the trade are, respectively:

Breakeven Price

Maximum Gain

A)                                        $24 $4

B)                                        $24 $3

C)                                        $27 unlimited

D)                                        $27 $4

The correct answer was A)

The breakeven price is the premium received on the call plus the strike price. For a writer of an option, the maximum gain is the premium received.

19.An investor bought a 40 put on a stock trading at 43 for a premium of $1. What is the maximum gain on the put and the value of the put at expiration if the stock price is $41?

Maximum Gain on Put

Value of the Put at Expiration

A)                                        $39 $0

B)                                        $40 $2

C)                                        unlimited       $1

D)                                        $42 $2

The correct answer was A)

The maximum gain on a long put is the strike price minus the premium, 40 – 1 = $39. The value at expiration is zero because the put is out-of-the-money.

20.An investor bought a 15 call for $14 on a stock trading at $20. If the stock is trading at $24 at option expiration, what is the profit and the value of the call at option expiration?

Profit

Value of the Call

A)                                        -$5 $5

B)                                        $4  -$5

C)                                        -$5 $9

D)                                        $1  $9

The correct answer was C)

The potential gains on a call purchase are unlimited. With a stock price of $24, the call at 15 is $9 in the money. By subtracting out the 14 call price a loss of $5 results.