Derivatives【 Reading 37】习题精选 continue, investor, 2012, believes

clearlycanadian

An investor believes that a stock they own will continue to oscillate in price and may trend downward in price. The best course of action for them to take would be to:

A) enter into both a covered call and protective put strategy.

B) sell call options on the stock.

C) buy put options on the stock.

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With a stock that is oscillating in price in which it is not trending upward, a covered call strategy is appropriate in which the investor owns the underlying asset and sells call options to enhance income. This strategy will work as long as the stock price does not go above the call strike price. In a downward trending market in which the investor believes the stock price will decrease, a protective put is appropriate in which they purchase a put on the underlying stock.

clearlycanadian

Assume a stock has a value of $100. Using at the money call and put options on that stock with 0.5 years to expiration and a constant interest rate of 6 percent, what is the necessary amount that needs to be invested in a zero coupon risk-free bond in order to synthetically replicate the underlying stock. Which of the following is closest to the correct answer?

A) $103.00.

B) $97.04.

C) $100.00.

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From put-call-parity the investment in the risk-free bond should be the present value of the exercise price of the call and the put. That is, Xe-rt = 100e-(0.06)(0.5) = 97.04.

clearlycanadian

A stock’s value on the date of option expiration is $88.50. For a call purchased with a $2.20 premium and an exercise price of $85, what is the breakeven price?

A) $86.30.

B) $87.20.

C) $88.50.

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The breakeven price is the exercise price plus the premium. The stock’s value on the date of expiration is not necessary information for this problem.

clearlycanadian

What is the expiration payoff of a long straddle, with an exercise price $100, if the underlying stock price is $125?

A) $25.

B) -$25.

C) $0.

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A long straddle consists of a long call and put with the same exercise price and the same expiration, at a stock price of $125 the put will expire worthless and the call value will be $25.

clearlycanadian

Assume that the current price of a stock is $100. A call option on that stock with an exercise price of $97 costs $7. A call option on the stock with the same expiration and an exercise price of $103 costs $3. Using these options what is the expiration profit of a bear call spread if the stock price is equal to $110?

A) -$6.

B) -$2.

C) $2.

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The trader of a bear call spread sells the call with an exercise price below the current stock price and buys the call option with an exercise price above the stock price. Therefore, for a stock price of $110 at expiration of the options, the buyer realizes a payoff of -$13 from his short position and a positive payoff of $7 from his long position for a net payoff of -$6. The revenue of the strategy is $4. Hence the profit is equal to -$2.

clearlycanadian

An investor purchases a stock for $38 and a put for $0.50 with a strike price of $35. The investor sells a call for $0.50 with a strike price of $40. What is the maximum profit and loss for this position?

A) infinite profit and maximum loss = -$4.00.

B) maximum profit = $2.00 and maximum loss = -$3.00.

C) maximum profit = $3.00 and maximum loss = -$4.00.

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The option position described is a zero cost collar. It is zero cost because the premium paid for the protective put is offset by the premium received for writing a covered call. The collar will put a band around the prospective returns by limiting the upside and downside of position. The upside will be limited by the strike price on the covered call ($40), while the downside will be limited by the strike price of the put ($35).

Maximum profit = $40 - $38 = $2
Maximum loss = $35 - $38 = -$3

clearlycanadian

The buyer of a straddle on a stock is most likely to benefit:

A) if the volatility of the underlying asset’s price decreases.

B) under all conditions because the straddle is guaranteed a risk-free rate of return.

C) if the volatility of the underlying asset’s price increases.

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The buyer of the straddle purchases both a call and a put. This position will benefit from large swings of the price of the underlying stock in either direction. If the position expires worthless, which occurs when the stock price stays flat, the investor will lose 100% of the investment. The payoff diagram is:

clearlycanadian

Assume that the current price of a stock is $100. A call option on that stock with an exercise price of $97 costs $7. A call option on the stock with the same expiration and an exercise price of $103 costs $3. Using these options what is the cost of entering into a long bull spread on this stock?

A) $1.

B) $0.

C) $4.

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The buyer of a bull spread buys the call with an exercise price below the current stock price and sells the call option with an exercise price above the stock price. The cost of the strategy is the difference between the cost of buying the option with the lower exercise price and selling the option with the higher exercise price which is $7 - $3 = $4 to enter into this strategy.