Question 1

Now extend the one-period binomial model to a two-period world.Answer questions.
-What is the hedge ratio if the stock goes down one period?
A)0.00
B)0.0725
C)1.00
D)0.73
E)none of the above

Accepted Answer

B

Question 2

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

Accepted Answer

As the number of time periods in a binomial model increases, the binomial probability of an up move approaches 0.5. This is because, over a large number of periods, the probability of an up move is balanced by the probability of a down move, resulting in an equal chance of either outcome.

Question 3

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

Accepted Answer

A

Question 4

Which of the following are not path-dependent options when the stock pays a constant dividend yield?
A)European calls and European puts
B)European calls and American puts
C)American puts and European puts
D)American puts and European calls
E)none of the above

Accepted Answer

When the stock pays a constant dividend yield, the value of the option is not path-dependent. Therefore, both European calls and European puts would not be path-dependent options. American options may have some path-dependency, but in this case, the fact that the stock pays a constant dividend yield would mitigate this effect.

Question 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?
A)the binomial tree will recombine
B)the binomial tree will not recombine
C)the option will be mispriced
D)an arbitrage profit will not be possible
E)none of the above

Accepted Answer

The answer of If the stock pays a specific dollar...

Question 6

In a non-recombining tree,the number of paths that will occur after three periods is
A)three
B)four
C)ten
D)eight
E)six

Accepted Answer

In a non-recombining tree, the number of paths after three periods can be calculated as 2^3 = 8, since each period can result in two outcomes (up or down), and these outcomes do not recombine.

Question 7

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 about a call with an exercise price of 80.
-What would be the call's price if the stock goes down?
A)8.00
B)3.60
C)0.00
D)9.00
E)none of the above

Accepted Answer

If the stock goes down by 8 percent, its new price would be 80 * (1 - 0.08) = 80 * 0.92 = 73.6. Since the exercise price of the call is 80, and the stock price is below this (73.6), the call would not be exercised because it's out of the money. Therefore, its value would be 0.00.

Question 8

Now extend the one-period binomial model to a two-period world.Answer questions.
-What is the current value of the call?
A)8.00
B)7.30
C)11.13
D)0.619
E)none of the above

Accepted Answer

The current value of the call can be calculated using the Black-Scholes formula with the provided inputs. Using the formula, the value of the call is approximately $7.30. Therefore, the best choice is B.

Question 9

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

Accepted Answer

As the number of time periods in a binomial model increases, the model approaches the Black-Scholes model, and the value of a European call option converges to a specific value calculated by the Black-Scholes formula. Therefore, the correct choice is B, converges to a specific value.

Question 10

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 about a call with an exercise price of 80.
-What is the hedge ratio?
A)0.429
B)0.714
C)0.571
D)0.823
E)none of the above

Accepted Answer

The answer of Consider a binomial world in which the...

Question 11

A portfolio that combines the underlying stock and a short position in an option is called
A)a risk arbitrage portfolio
B)a hedge portfolio
C)a ratio portfolio
D)a two-state portfolio
E)none of the above

Accepted Answer

A portfolio that combines the underlying stock and a short position in an option is designed to minimize risk and is therefore called a hedge portfolio. The short option position acts as an insurance against potential losses in the underlying stock, providing a good balance between risk and return. A risk arbitrage portfolio involves buying and selling stocks to take advantage of price discrepancies in different markets, while a ratio portfolio involves using options to adjust the exposure to the underlying stock market. A two-state portfolio is a type of investment strategy that involves investing in both high-risk assets and low-risk assets for diversification.

Question 12

When puts are priced with the binomial model,which of the following is true?
A)the puts must be American
B)the puts cannot be properly hedged
C)the puts will violate put-call parity
D)the hedge ratio is one throughout the tree
E)none of the above

Accepted Answer

The binomial model can be used to price both American and European puts, allows for proper hedging, does not inherently violate put-call parity, and the hedge ratio varies throughout the tree. Therefore, none of the given statements are true about puts priced with the binomial model.

Question 13

In the binomial model,if an option has no chance of expiring out-of-the-money,the hedge ratio will be
A)0.5
B)infinite
C)1
D)0
E)none of the above

Accepted Answer

The hedge ratio is calculated as the change in the option price divided by the change in the underlying asset price. If an option has no chance of expiring out-of-the-money, it means that it will definitely be exercised and its price will be equal to the difference between the stock price and the strike price. Therefore, the change in the option price will be equal to the change in the stock price. As a result, the hedge ratio will be 1, because the change in the option price and stock price will be the same.

Question 14

Suppose S = 70,X = 65,r = 0.05,p = 0.6,C_u = 7.17,C_d = 1.22 and there is one period left in an American call's life.What will the option be worth? A)6.83 B)0.00 C)4.56 D)5.00 E)none of the above

Accepted Answer

The answer of Suppose S = 70,X = 65,r =...

Question 15

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 about a call with an exercise price of 80.
-What would be the call's price if the stock goes up?
A)3.60
B)8.00
C)5.71
D)4.39
E)none of the above

Accepted Answer

If the stock goes up by 10 percent, its new price would be 80 * 1.10 = 88. The call option allows buying at 80, so the value if the stock goes up is 88 - 80 = 8.

Question 16

The values of u and d are which of the following?
A)the return on the stock if it goes up and down,respectively
B)the inverse of the ratio of the up and down probabilities,respectively,and the risk-free rate
C)the normal probabilities of up and down movements,respectively
D)one plus the return on the stock if it goes up and down,respectively
E)none of the above

Accepted Answer

The answer of The values of u and d are...

Question 17

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

Accepted Answer

If the call price in the market is higher than the call price given by the model, it indicates that the call is overvalued in the market. Therefore, you should sell the overvalued call and hedge by buying the stock, which is option C. This strategy profits from the call's overvaluation while hedging against movements in the stock's price.

Question 18

If the binomial model is extended to multiple periods for a fixed option life,which of the following adjustments must be made?
A)the up and down factors must be increased
B)the risk-free rate must be increased
C)the up and down factors and the risk-free rate must be decreased
D)the initial stock price must be proportionately reduced
E)none of the above

Accepted Answer

The answer of If the binomial model is extended to...

Question 19

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 about a call with an exercise price of 80.
-What is the theoretical value of the call?
A)8.00
B)4.39
C)5.15
D)5.36
E)none of the above

Accepted Answer

The answer of Consider a binomial world in which the...

Question 20

Now extend the one-period binomial model to a two-period world.Answer questions.
-What is the value of the call if the stock goes up,then down?
A)0.96
B)16.80
C)8.00
D)0.00
E)none of the above

Accepted Answer

The answer of Now extend the one-period binomial model to...

Quiz 4: Option Pricing Models: the Binomial Model

Now extend the one-period binomial model to a two-period world.Answer questions. -What is the hedge ratio if the stock goes down one period?

When the number of time periods in a binomial model is large,what happens to the binomial probability of an up move?

In a two-period binomial world,a mispriced call will lead to an arbitrage profit if

Which of the following are not path-dependent options when the stock pays a constant dividend yield?

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?

In a non-recombining tree,the number of paths that will occur after three periods is

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 about a call with an exercise price of 80. -What would be the call's price if the stock goes down?

Now extend the one-period binomial model to a two-period world.Answer questions. -What is the current value of the call?

When the number of time periods in a binomial model is large,a European call option value does what?

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 about a call with an exercise price of 80. -What is the hedge ratio?

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

When puts are priced with the binomial model,which of the following is true?

In the binomial model,if an option has no chance of expiring out-of-the-money,the hedge ratio will be

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?

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 about a call with an exercise price of 80. -What would be the call's price if the stock goes up?

The values of u and d are which of the following?

In a binomial model,if the call price in the market is higher than the call price given by the model,you should

If the binomial model is extended to multiple periods for a fixed option life,which of the following adjustments must be made?

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 about a call with an exercise price of 80. -What is the theoretical value of the call?

Now extend the one-period binomial model to a two-period world.Answer questions. -What is the value of the call if the stock goes up,then down?

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