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:
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A) |
the intrinsic put value is $0 and the put is at-the-money. | |
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B) |
the intrinsic call value is $1. | |
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C) |
if Grey exercises, he will have gained a total of $4.75. | |
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. 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.
Which of the following statements about the investors is least accurate?
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A) |
Grey's loss is unlimited. | |
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B) |
Grey's maximum gain and Kishiro's maximum loss sum to zero. | |
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C) |
Kishiro's gain is limited to the strike price minus the premium. | |
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.
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发表于 2010-4-26 23:01
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