An Introduction To Derivatives And Risk Management 10th Edition By Don M. – Test Bank
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CHAPTER
4: OPTION PRICING MODELS: THE BINOMIAL MODEL
MULTIPLE CHOICE TEST QUESTIONS
1. A
portfolio that combines the underlying stock and a short position in an option
is called
2. a
risk arbitrage portfolio
3. a
hedge portfolio
4. a
ratio portfolio
5. a
two-state portfolio
6. none
of the above
2. In a
binomial model, if the call price in the market is higher than the call price
given by the model, you should
3. sell
the call and sell short the stock
4. buy
the call and sell short the stock
5. buy
the stock and sell the call
6. buy
the call and buy the stock
7. none
of the above
3. In a
two-period binomial world, a mispriced call will lead to an arbitrage profit if
4. the
proper hedge ratio is maintained over the two periods
5. the
hedge portfolio is terminated after one period
6. the
option goes from over- to underpriced or vice versa
7. the
option remains mispriced over both periods
8. none
of the above
4. The values
of u and d are which of the following?
5. the
return on the stock if it goes up and down, respectively
6. the
inverse of the ratio of the up and down probabilities, respectively, and the
risk-free rate
7. the
normal probabilities of up and down movements, respectively
8. one
plus the return on the stock if it goes up and down, respectively
9. none
of the above
5. 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?
6. the
binomial tree will recombine
7. the
binomial tree will not recombine
8. the
option will be mispriced
9. an
arbitrage profit will not be possible
10. none
of the above
6. When
puts are priced with the binomial model, which of the following is true?
7. the
puts must be American
8. the
puts cannot be properly hedged
9. the
puts will violate put-call parity
10. the
hedge ratio is one throughout the tree
11. none
of the above
7. If
the binomial model is extended to multiple periods for a fixed option life,
which of the following adjustments must be made?
8. the
up and down factors must be increased
9. the
risk-free rate must be increased
10. the
up and down factors and the risk-free rate must be decreased
11. the
initial stock price must be proportionately reduced
12. none
of the above
8. Which
of the following are not path-dependent options when the stock pays a constant
dividend yield?
9. European
calls and European puts
10. European
calls and American puts
11. American
puts and European puts
12. American
puts and European calls
13. none
of the above
9. In a non-recombining
tree, the number of paths that will occur after three periods is
10. three
11. four
12. ten
13. eight
14. six
10. When
the number of time periods in a binomial model is large, a European call option
value does what?
11. fluctuates
around its intrinsic value
12. converges
to a specific value
13. increases
without limit
14. converges
to the European lower bound
15. none
of the above
11. When
the number of time periods in a binomial model is large, what happens to the
binomial probability of an up move?
12. it
approaches 1.0
13. it approaches
zero
14. it
fluctuates without pattern
15. it
converges to 0.5
16. 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 risk-free rate is 4
percent. Assume a one-period world. Answer questions 12 through 15 about a call
with an exercise price of 80.
12. What
would be the call’s price if the stock goes up?
13. 3.60
14. 8.00
15. 5.71
16. 4.39
17. none
of the above
13. What
would be the call’s price if the stock goes down?
14. 8.00
15. 3.60
16. 0.00
17. 9.00
18. none
of the above
14. What
is the hedge ratio?
15. 0.429
16. 0.714
17. 0.571
18. 0.823
19. none
of the above
15. What
is the theoretical value of the call?
16. 8.00
17. 4.39
18. 5.15
19. 5.36
20. none
of the above
Now extend the one-period binomial model to a two-period world.
Answer questions 16 through 18.
16. What
is the value of the call if the stock goes up, then down?
17. 0.96
18. 16.80
19. 8.00
20. 0.00
21. none
of the above
17. What
is the hedge ratio if the stock goes down one period?
18. 0.00
19. 0.0725
20. 1.00
21. 0.73
22. none
of the above
18. What
is the current value of the call?
19. 8.00
20. 7.30
21. 11.13
22. 0.619
23. none
of the above
19. In
the binomial model, if an option has no chance of expiring out-of-the-money,
the hedge ratio will be
20. 0.5
21. infinite
22. 1
23. 0
24. none
of the above
20. 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?
21. 6.83
22. 0.00
23. 4.56
24. 5.00
25. none
of the above
21. In a
one-period 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?
22. 2.17
23. 0.50
24. 9.50
25. 5.00
26. none
of the above
22. Which
of the following statements about the binomial model is incorrect?
23. it
converges to the Black-Scholes-Merton model
24. it
can accommodate early exercise
25. it
allows only two stock prices at expiration
26. it
can be extended to a large number of time periods
27. none
of the above
23. A
stock priced at 50 can go up or down by 10 percent over two periods. The
risk-free rate is 4 percent. Which of the following is the correct price of an
American put with an exercise price of 55?
24. 88
25. 38
26. 00
27. 00
28. 65
24. 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 risk-free rate.
25. 22
26. 48
27. 40
28. 32
29. none
of the above
25. Which
of the following statements about the binomial option pricing model is not
always true?
26. it
can capture the effect of early exercise
27. it
can accommodate a large number of possible stock prices at expiration
28. it
reflects the effects of the stock price, exercise price, risk-free 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
26. All
of the following are variables used to determine a call option’s price except
27. the risk-free
rate
28. the
probability of stock price movement
29. the
exercise price
30. the
possible future stock prices at expiration
31. none
of the above
27. Pricing
a put with the binomial model is the same procedure as pricing with a call,
except that the
28. underlying
stock must not pay dividends
29. binomial
model cannot account for expiration payoffs
30. value
of the underlying must be discounted back to the current time period
31. expiration
payoffs reflect the fact that the option is the right to sell the underlying
stock
32. none
of the above
28. All
of the following are practical applications of the binomial model except
29. choices
regarding real options
30. options
regarding executive incentive plans
31. models
in which the stock price can go up, down, or remain constant in the next period
32. embedded
options within debt securities
33. none
of the above
29. Determine
the value of d for a four period binomial model when the option’s life is
one-fourth of a year and the volatility is 0.64. Use the model for u and d that
does not require the risk-free rate.
30. 0.85
31. 1.17
32. 2.56
33. 0.90
34. none
of the above
30. The
binomial option pricing model will converge to what value as the number of
periods increases?
31. a
random value
32. the
Black-Scholes-Merton value of the option
33. the
intrinsic volatility of the option
34. the
true value of the underlying
35. none
of the above
CHAPTER
4: OPTION PRICING MODELS: THE BINOMIAL MODEL
TRUE-FALSE 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 risk-free 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 in-the-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 path-independent.
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 risk-free 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 risk-free
discount rate is adjusted.
T
F
27. In a non-recombining 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 risk-free rate.
T
F
30. Put-call 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 risk-free 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 Black-Scholes 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.
1. How
much will the spread cost?
2. $986
3. $302
4. $283
5. $193
6. none
of the above
2. What
is the maximum profit on the spread?
3. $500
4. $802
5. $198
6. $302
7. none
of the above
3. What
is the maximum loss on the spread?
4. $500
5. $698
6. $198
7. $802
8. none
of the above
4. What
is the profit if the stock price at expiration is $47?
5. -$102
6. $398
7. -$302
8. $500
9. none
of the above
5. What
is the breakeven point?
6. $48.02
7. $41.98
8. $55.66
9. $50.00
10. none
of the above
6. Suppose
you closed the spread 60 days later. What will be the profit if the stock price
is still at $50?
7. $41
8. $198
9. $302
10. $102
11. 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.
7. What
will be the cost of the butterfly spread?
8. $1,195
9. $637
10. $79
11. $1,045
12. none
of the above
8. What
will be the profit if the stock price at expiration is $52.50?
9. $171
10. $1,421
11. $1.037
12. $421
13. none
of the above
9. 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?
10. 105
11. 95
12. 100
13. 57
14. 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. What
will the spread cost?
11. -$176
12. $176
13. $558
14. $105
15. none
of the above
11. What
will be the profit if the spread is held 90 days and the stock price is $45?
12. $36
13. $20
14. $558
15. -$20
16. none
of the above
Answer questions 12 through 17 about a long straddle constructed
using the June 50 options.
12. What
will the straddle cost?
13. $145
14. $690
15. $971
16. $413
17. none
of the above
13. What
are the two breakeven stock prices at expiration?
14. $55.58
and $45.87
15. $54.13
and $45.87
16. $55.58
and $44.42
17. $59.71
and $40.29
18. none
of the above
14. What
is the profit if the stock price at expiration is at $64.75?
15. -$971
16. $1,475
17. -$3,525
18. $500
19. none
of the above
15. What
is the profit if the position is held for 90 days and the stock price is $55?
16. -$971
17. -$58
18. -$109
19. -$471
20. none
of the above
16. 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?
17. lower
both the upside and downside breakevens
18. raise
both the upside and downside breakevens
19. raise
the upside and lower the downside breakevens
20. lower
the upside and raise the downside breakevens
21. none
of the above
17. 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.
18. -$129
19. $1,416
20. $429
21. $1,384
22. none
of the above
Answer questions 18 through 20 about a long box spread using the
June 50 and 55 options.
18. What
is the cost of the box spread?
19. $500
20. $2,018
21. $76
22. $484
23. none
of the above
19. What
is the profit if the stock price at expiration is $52.50?
20. $16
21. $500
22. –$234
23. $250
24. none
of the above
20. What
is the net present value of the box spread?
21. $9.84
22. $5.00
23. $16.00
24. $1.84
25. none
of the above
21. Which
of the following strategies does not profit in a rising market?
22. put bull
spread
23. long
straddle
24. collar
25. call
bull spread
26. none
of the above
22. Which
of the following transactions can have an unlimited loss?
23. long
straddle
24. calendar
spread
25. butterfly
spread
26. reverse
box spread
27. none
of the above
23. Which
of the following is the best strategy for an expected fall in the market?
24. long
strip (2 puts and 1 call)
25. put
bull spread
26. calendar
spread
27. butterfly
spread
28. none
of the above
24. Early
exercise is a disadvantage in which of the following transactions?
25. short
box spread
26. put
bear spread
27. long
strip (2 puts and 1 call)
28. long
strap (2 calls and 1 put)
29. none
of the above
25. Which
of the following have similar profit graphs?
26. call
bull spread and long box spread
27. put
bear spread and short box spread
28. butterfly
spread and ratio spread
29. calendar
spread and call bear spread
30. none
of the above
26. The
purchase of one option and the sale of another is known as
27. box
28. bear
strategy
29. bull
strategy
30. collar
31. spread
27. 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
28. box
29. bear
strategy
30. bull
strategy
31. collar
32. spread
28. The
profit from a put bear spread strategy when both options are out of the money
is
29. –X1 +
ST + P1 + X2 –
ST – P2
30. –X1 +
ST + P1 – P2
31. X1 –
ST – P1 – X2 +
ST + P2
32. P1 +
X2 – ST – P2
33. P1 –
P2
29. “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?
30. volatility
31. expected
rate of return
32. beta
33. correlation
with the benchmark index
34. skewness
30. Which
of the following statements best describes the nature of option time value
decay?
31. time value
decays more rapidly as the stock price approaches being at-the-money
32. time
value decays more rapidly as expiration approaches
33. time
value decays more rapidly for put option than call options
34. time
value decay does not occur for collar option strategies
35. 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 in-the-money 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 zero-cost collar option strategy when the terminal stock price ends up in
between the two strike prices is ST –
S0 where X2 >
X1.
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