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.

optiix

All of the following are conditions that make the second-order gamma effect more important to a manager delta-hedging an option EXCEPT when the:

A) delta is near zero.

B) option is at-the-money.

C) option is near expiration.

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All of these conditions make the gamma effect more important except the delta being near zero. If the delta is near zero or one then the option delta will move more slowly towards zero or one and cause less of an affect on gamma.

optiix

In delta-hedging, gamma would be important if the price of the underlying asset:

A) had a large move upward only.

B) remained constant.

C) had a large move upward or downward.

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Gamma refers to the change in value of delta given the change in value of the underlying stock. Typically, larger swings in the price of an asset will cause larger changes in delta, thus impacting the delta hedge. This means that the larger the move in the underlying asset in either direction, the more important is the second-order gamma effect.

optiix

In delta-hedging a call position, which of the following pairs of conditions would lead to the gamma effect being the most important? The call is:

A) at-the-money and has a long time until expiration.

B) out-of-the-money and near expiration.

C) at-the-money and near expiration.

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Gamma refers to the change in value of the delta given the change in value of the underlying stock. Gamma will be most important when the call option being hedged is either at the money or near expiration.

optiix

An option dealer is delta hedging a short call position on a stock. As the stock price increases, in order to maintain the hedge, the dealer would most likely have to:

A) buy T-bills.

B) sell some the shares of the stock.

C) buy more shares of the stock.

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As the value of the underlying increases, the delta of a call option increases. This means more of the underlying asset is needed to hedge the position.

optiix

A short position in naked calls on an asset can be delta hedged by:

A) shorting the underlying asset.

B) buying the put.

C) buying the underlying asset.

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Delta hedging a naked call can be accomplished by owning the underlying asset in an amount that will make the value of the short-call/long-asset portfolio immune to changes in the price of the underlying asset.

optiix

A manager would delta hedge a position to:

A) earn extra “dividend” income on a given position.

B) earn the risk-free rate.

C) place a floor on the position while leaving the potential for upside risk.

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A delta hedged position should earn the risk-free rate. The position does not earn a “dividend” although it should increase in value gradually (at the risk-free rate). The upside potential is limited to the risk-free rate. The manager would have to constantly monitor and adjust the position to achieve the goal.

optiix

A firm purchases a one-year cap with a strike rate of 4%, a notional principal of $3 million, and semiannual settlement. The reference rate at the initiation of the cap is 5%, falls to 4.5% at the next settlement and then to 4% one year after the cap’s initiation. The total payoffs (without discounting) over the maturity of the swap would be:

A) $22,792.

B) $25,500.

C) $7,583.

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Since the number of days is not given for each period, approximate it with 182 in the first period and 183 in the second period. Remember that payments are made in arrears.

First payoff = $ 15,167 = $3,000,000 × max(0, 0.05 – 0.04) × (182/360).
Second payoff = $7,625 = $3,000,000 × max(0, 0.045 – 0.04) × (183/360)
Total = $22,792 = $7,625 + $ 15,167

optiix

Which of the following is equivalent to a pay-fixed interest rate swap?

A) Buying a cap and selling a floor.

B) Buying a cap and selling an interest rate collar.

C) Selling a cap and buying a floor.

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A pay-fixed interest rate swap has the same payoffs as a long position in the corresponding interest rate collar (with the strike rate equal to the swap fixed rate).

optiix

A firm purchases a collar with floor rate of 3% and a cap rate of 4.4%. The cap and floor have quarterly settlement and a notional principal of $10 million. The maximum outflow and inflow the buyer can expect on a given settlement is (assume equal settlement periods):

A) $110,000 and maximum inflow = $140,000.

B) $75,000 and maximum inflow = $140,000.

C) $75,000 and maximum inflow = infinite.

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Given the possible answers, this must be a collar consisting of a short floor and long cap. The firm’s maximum outflow would occur from the floor when the reference rate is zero: $10,000,000 × (0.03 − 0) / 4 = $75,000. Although interest rates cannot go to infinity, there is no upper limit on what the owner can expect from the cap. Thus “infinite” is the best answer.