An Introduction To Derivatives And Risk Management 10th Edition By Don M. – Test Bank

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Sample Questions

CHAPTER 4: OPTION PRICING MODELS: THE BINOMIAL MODEL

MULTIPLE CHOICE TEST QUESTIONS

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4.

A portfolio that combines the underlying stock and a short position in an option is called a risk arbitrage portfolio a hedge portfolio a ratio portfolio

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a two­state portfolio none of the above

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In a binomial model, if the call price in the market is higher than the call price given by the model, you should sell the call and sell short the stock buy the call and sell short the stock buy the stock and sell the call buy the call and buy the stock none of the above

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In a two­period binomial world, a mispriced call will lead to an arbitrage profit if the proper hedge ratio is maintained over the two periods the hedge portfolio is terminated after one period the option goes from over­ to underpriced or vice versa the option remains mispriced over both periods none of the above

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9.

The values of u and d are which of the following? the return on the stock if it goes up and down, respectively the inverse of the ratio of the up and down probabilities, respectively, and the risk­free rate the normal probabilities of up and down movements, respectively one plus the return on the stock if it goes up and down, respectively none of the above

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If the stock pays a specific dollar dividend and the stock price, to include the dividend, follows the binomial up and down factors, which of the following will happen? the binomial tree will recombine the binomial tree will not recombine the option will be mispriced an arbitrage profit will not be possible none of the above

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11.

When puts are priced with the binomial model, which of the following is true? the puts must be American the puts cannot be properly hedged the puts will violate put­call parity the hedge ratio is one throughout the tree none of the above

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If the binomial model is extended to multiple periods for a fixed option life, which of the following adjustments must be made? the up and down factors must be increased the risk­free rate must be increased the up and down factors and the risk­free rate must be decreased the initial stock price must be proportionately reduced none of the above

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Which of the following are not path­dependent options when the stock pays a constant dividend yield?

European calls and European puts European calls and American puts American puts and European puts American puts and European calls none of the above

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In a non­recombining tree, the number of paths that will occur after three periods is three four ten eight six

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When the number of time periods in a binomial model is large, a European call option value does what? fluctuates around its intrinsic value converges to a specific value increases without limit converges to the European lower bound none of the above

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When the number of time periods in a binomial model is large, what happens to the binomial probability of an up move? it approaches 1.0 it approaches zero it fluctuates without pattern it converges to 0.5 none of the above

Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk­free rate is 4 percent. Assume a one­period world. Answer questions 12 through 15 about a call with an exercise price of 80.

12.

13.

14.

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16.

17.

What would be the call’s price if the stock goes up?

3.60 8.00 5.71 4.39 none of the above

13.

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18.

What would be the call’s price if the stock goes down?

8.00 3.60 0.00 9.00 none of the above

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19.

What is the hedge ratio?

0.429 0.714 0.571 0.823 none of the above

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What is the theoretical value of the call?

8.00 4.39 5.15 5.36 none of the above

Now extend the one­period binomial model to a two­period world. Answer questions 16 through 18.

16.

17.

18.

19.

What is the value of the call if the stock goes up, then down?

0.96 16.80 8.00

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21.

0.00 none of the above

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18.

19.

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22.

What is the hedge ratio if the stock goes down one period?

0.00 0.0725 1.00 0.73 none of the above

18.

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What is the current value of the call?

8.00 7.30 11.13 0.619 none of the above

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In the binomial model, if an option has no chance of expiring out­of­the­money, the hedge ratio will be 0.5 infinite 1 0 none of the above

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Suppose S = 70, X = 65, r = 0.05, p = 0.6, Cu = 7.17, Cd = 1.22 and there is one period left in an American call’s life. What will the option be worth?

6.83 0.00 4.56 5.00 none of the above

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26.

In a one­period binomial model with Su = 49.5, Sd = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?

2.17 0.50 9.50 5.00 none of the above

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Which of the following statements about the binomial model is incorrect? it converges to the Black­Scholes­Merton model it can accommodate early exercise it allows only two stock prices at expiration it can be extended to a large number of time periods none of the above

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A stock priced at 50 can go up or down by 10 percent over two periods. The risk­free rate is 4 percent. Which of the following is the correct price of an American put with an exercise price of 55?

88 38 00 00 65

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Determine the value of u for a three period binomial problem when the option’s life is one­ half a year and the volatility is 0.48. Use the model for u that does not require the risk­free rate.

22 48 40 32 none of the above

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Which of the following statements about the binomial option pricing model is not always true? it can capture the effect of early exercise it can accommodate a large number of possible stock prices at expiration it reflects the effects of the stock price, exercise price, risk­free rate, volatility and time to expiration 29. it gives the price at which the option will trade in the market.

30. none of the above

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All of the following are variables used to determine a call option’s price except the risk­free rate the probability of stock price movement the exercise price the possible future stock prices at expiration none of the above Pricing a put with the binomial model is the same procedure as pricing with a call, except that the

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underlying stock must not pay dividends binomial model cannot account for expiration payoffs value of the underlying must be discounted back to the current time period expiration payoffs reflect the fact that the option is the right to sell the underlying stock none of the above All of the following are practical applications of the binomial model except choices regarding real options options regarding executive incentive plans models in which the stock price can go up, down, or remain constant in the next period embedded options within debt securities none of the above Determine the value of d for a four period binomial model when the option’s life is one­fourth of a year and the volatility is 0.64. Use the model for u and d that does not require the risk­free rate.

0.85 1.17 2.56 0.90 none of the above The binomial option pricing model will converge to what value as the number of periods increases? a random value the Black­Scholes­Merton value of the option the intrinsic volatility of the option the true value of the underlying none of the above

CHAPTER 4: OPTION PRICING MODELS: THE BINOMIAL MODEL

TRUE­FALSE TEST QUESTIONS

T F 1. The binomial model assumes that investors are risk neutral.

T F 2. The hedge ratio is the number of shares per call in a risk­free portfolio.

T F 3. In the binomial model, if a call is overpriced, investors should sell it and buy stock.

T F 4. One way to model an option with dividends in the binomial framework is for the stock price minus the present value of the dividends to grow by the up and down factors.

T F 5. A riskless hedge involving stock and puts requires a long position in stock and a short position in puts.

T F 6. The up and down factors in the binomial model are analogous to the volatility.

T F 7. In a recombining binomial model with n periods, the number of outcomes is n + 1.

T F 8. When the hedge ratio is adjusted in the binomial model, the transactions must be done in the option.

T F 9. The binomial probabilities are probabilities if investors were risk neutral.

T F 10. If there is one period remaining and no possibility of the option expiring in­the­ money, the hedge ratio will be zero.

T F 11. When pricing a put with the binomial model, the up and down probabilities are reversed.

T F 12. When pricing an American put with the binomial model, you must check for early exercise at each time point and stock price except the current one.

T F 13. If the binomial model is used with a specific dollar dividend and the stock price follows the up and down parameters, the tree will explode and end up with far more outcomes than time periods.

T F 14. Options that can be priced by considering only the payoffs at expiration are called path­independent.

T F 15. Over a large number of periods, the up and down parameters move closer to 1.5 and 0.5, respectively.

T F 16. If the number of binomial periods is increased and u, d and r are not adjusted, the value of a European call will increase.

T F 17. The binomial option pricing formula is based on the weighted average of the next two possible values, discounted back to the present.

T F 18. If a call is overpriced and you buy the call and sell short the stock, it is equivalent to investing money at less than the risk­free rate.

T F 19. If the binomial model describes the real world, the combined actions of all investors will cause the market price to converge to the binomial price.

T F 20. In a multiperiod binomial model, an arbitrage profit cannot be earned until the option expires.

T F 21. The formula for a hedge ratio of a put is the same as that of the call, except that put prices are used instead of call prices.

T F 22. The binomial model will give a higher price for an American call on a stock that pays no dividends than if that call is European.

T F 23. If the stock price adjusted for dividends at a continuous rate follows the up and down parameters, the binomial tree will recombine.

T F 24. The binomial option pricing formula will conform to the European lower bound.

T F 25. When calls are sold to adjust the hedge ratio, the funds must be placed in additional shares.

T F 26. The binomial model for foreign currency options is similar to the binomial model for stock options except the risk­free discount rate is adjusted.

T F 27. In a non­recombining binomial model with n periods, the number of outcomes is 2n.

T F 28. The single period binomial hedge ratio for stock call options could be computed by equating the two future cash flows — from a portfolio of long h shares of stock and short one call — and solve for the number of underlying stocks to hold.

T F 29. If a call is underpriced and you buy the call and sell short the stock, it is equivalent to investing money at more than the risk­free rate.

T F 30. Put­call parity holds within a two period binomial model.

CHAPTER 7: ADVANCED OPTION STRATEGIES

MULTIPLE CHOICE TEST QUESTIONS

The following prices are available for call and put options on a stock priced at $50. The risk­free rate is 6 percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180 days remaining. The Black­Scholes model was used to obtain the prices.

Calls

Puts

Strike

March

June

March

June

45

6.84

8.41

1.18

2.09

50

3.82

5.58

3.08

4.13

55

1.89

3.54

6.08

6.93

Use this information to answer questions 1 through 20. Assume that each transaction consists of one contract (for 100 shares) unless otherwise indicated.

For questions 1 through 6, consider a bull money spread using the March 45/50 calls.

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How much will the spread cost? $986 $302 $283 $193 none of the above

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7.

What is the maximum profit on the spread? $500 $802 $198 $302 none of the above

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4.

What is the maximum loss on the spread? $500

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7.

8.

$698 $198 $802 none of the above

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9.

What is the profit if the stock price at expiration is $47? ­$102 $398 ­$302 $500 none of the above

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10.

What is the breakeven point? $48.02 $41.98 $55.66 $50.00 none of the above

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11.

Suppose you closed the spread 60 days later. What will be the profit if the stock price is still at $50? $41 $198 $302 $102 none of the above

For questions 7 and 8, suppose an investor expects the stock price to remain at about $50 and decides to execute a butterfly spread using the June calls.

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What will be the cost of the butterfly spread? $1,195 $637 $79 $1,045 none of the above

8.

What will be the profit if the stock price at expiration is $52.50?

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$171 $1,421 $1.037 $421 none of the above

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11.

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14.

Suppose you wish to construct a ratio spread using the March and June 50 calls. You want to buy 100 June 50 call contracts. How many March 50 calls would you sell?

105 95 100 57 none of the above

Answer questions 10 and 11 about a calendar spread based on the assumption that stock prices are expected to remain fairly constant. Use the June/March 50 call spread. Assume one contract of each.

10.

11.

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What will the spread cost? ­$176 $176 $558 $105 none of the above

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What will be the profit if the spread is held 90 days and the stock price is $45? $36 $20 $558 ­$20 none of the above

Answer questions 12 through 17 about a long straddle constructed using the June 50 options.

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What will the straddle cost? $145 $690 $971

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$413 none of the above

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What are the two breakeven stock prices at expiration? $55.58 and $45.87 $54.13 and $45.87 $55.58 and $44.42 $59.71 and $40.29 none of the above

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What is the profit if the stock price at expiration is at $64.75? ­$971 $1,475 ­$3,525 $500 none of the above

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20.

What is the profit if the position is held for 90 days and the stock price is $55? ­$971 ­$58 ­$109 ­$471 none of the above

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21.

Suppose the investor adds a call to the long straddle, a transaction known as a strap. What will this do to the breakeven stock prices? lower both the upside and downside breakevens raise both the upside and downside breakevens raise the upside and lower the downside breakevens lower the upside and raise the downside breakevens none of the above

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Suppose a put is added to a straddle. This overall transaction is called a strip. Determine the profit at expiration on a strip if the stock price at expiration is $36. ­$129 $1,416 $429 $1,384 none of the above

Answer questions 18 through 20 about a long box spread using the June 50 and 55 options.

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What is the cost of the box spread? $500 $2,018 $76 $484 none of the above

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What is the profit if the stock price at expiration is $52.50? $16 $500 –$234 $250 none of the above

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25.

What is the net present value of the box spread? $9.84 $5.00 $16.00 $1.84 none of the above

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26.

Which of the following strategies does not profit in a rising market? put bull spread long straddle collar call bull spread none of the above

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27.

Which of the following transactions can have an unlimited loss? long straddle calendar spread butterfly spread reverse box spread none of the above

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Which of the following is the best strategy for an expected fall in the market? long strip (2 puts and 1 call) put bull spread calendar spread butterfly spread none of the above

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Early exercise is a disadvantage in which of the following transactions? short box spread put bear spread long strip (2 puts and 1 call) long strap (2 calls and 1 put) none of the above

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30.

Which of the following have similar profit graphs? call bull spread and long box spread put bear spread and short box spread butterfly spread and ratio spread calendar spread and call bear spread none of the above

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31.

The purchase of one option and the sale of another is known as box bear strategy bull strategy collar spread

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The option strategy where the holder of a long position in a stock buys a put with an exercise price lower than the current stock price and sells a call with an exercise price higher than the current stock price is known as box bear strategy bull strategy collar spread

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30.

The profit from a put bear spread strategy when both options are out of the money is –X1 + ST + P1 + X2 – ST – P2 –X1 + ST + P1 – P2

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X1 – ST – P1 – X2 + ST + P2 P1 + X2 – ST – P2 P1 – P2

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“Like the butterfly spread, the calendar spread is one in which the underlying instrument’s ___________ is the major factor in its performance.” The best word for the blank is which of the following? volatility expected rate of return beta correlation with the benchmark index skewness

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Which of the following statements best describes the nature of option time value decay? time value decays more rapidly as the stock price approaches being at­the­money time value decays more rapidly as expiration approaches time value decays more rapidly for put option than call options time value decay does not occur for collar option strategies time value decay is detrimental for a trader who is short call options

CHAPTER 7: ADVANCED OPTION STRATEGIES

TRUE/FALSE TEST QUESTIONS

T F 1. A spread that is profitable if the options are in­the­money is called a money spread.

T F 2. Buying a put money spread is a bearish strategy.

T F 3. In a calendar spread the time value of the nearby option will decay more rapidly.

T F 4. A call bear spread is a strategy for investors who expect stock prices to increase.

T F 5. A call money spread that is closed prior to expiration has lower losses but higher profits for each stock price than if held to expiration.

T F 6. There are three breakeven stock prices in a butterfly spread.

T F 7. Early exercise is an important risk when call bear spreads and put bull spreads are used.

T F 8. A call butterfly spread combines a call bull spread with a call bear spread.

T F 9. A call butterfly spread is a bullish strategy that is profitable if stock prices increase.

T F 10. A reverse calendar spread is used to take advantage of unexpected high volatility.

T F 11. One of the risks of a calendar spread is that the intrinsic values may be different.

T F 12. The holder of a straddle does not care which way the market moves as long as it makes a significant move.

T F 13. If a straddle is closed prior to expiration, the investor can recover some of the time value of either the call or the put but not both.

T F 14. An investor who holds a strap (2 calls and 1 put) believes the market is more likely to go up than down.

T F 15. A strip (2 puts and one call) would cost more than a straddle but would pay off more if the stock falls.

T F 16. The payoffs form a straddle are more like the payoffs from a money spread than a calendar spread.

T F 17. The risk of early exercise is of no concern to the holder of a long straddle.

T F 18. At the expiration of a box spread, at most there will be only one option exercised.

T F 19. A box spread is a combination of a call bull spread and a put bear spread.

T F 20. A box spread is a good strategy to use if high volatility is expected.

T F 21. The delta of a straddle would be the call delta plus the put delta.

T F 22. A strap is a less expensive bullish strategy than a straddle.

T F 23. A collar gives downside protection, leaving the upside open.

T F 24. A ratio spread can be conducted with money spreads or time spreads.

T F 25. To truly gain from a straddle, an investor must have a better estimate of volatility than everyone else.

T F 26. A spread option strategy is a transaction in one option and an opposite transaction in the underlying instrument.

T F 27. The profit from a collar option strategy when the terminal stock price ends up in between the two strike prices is ST – S0 – P1 + C2 where X2 > X1.

T F 28. The longer an investor holds a long call butterfly spread position, everything else the same, the greater the distance between the breakeven stock prices.

T F 29. The breakeven points for a long straddle strategy are equidistant from the current stock price regardless of the chosen strike price.

T F 30. The profit from a zero­cost collar option strategy when the terminal stock price ends up in between the two strike prices is ST – S0 where X2 > X1.