Deck 4: Option Pricing Models: the Binomial Model

Question 1

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

Answer 1

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
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.

Answer 2

D

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

Answer 3

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

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

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

Question 7

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

Question 8

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

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

Question 10

What is the hedge ratio?

A)0.429
B)0.714
C)0.571
D)0.823
E)none of the above

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

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

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

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

Question 15

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

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

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)buy the stock and sell the call

A)sell the call and sell short the stock
B)buy the call and buy the stock
B)buy the call and sell short the stock
C)none of the above

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

Question 19

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
Now extend the one-period binomial model to a two-period world.Answer questions 16 through 18.

Question 20

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

Question 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?

A)2.17
B)0.50
C)9.50
D)5.00
E)none of the above

Question 22

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.

Question 23

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

Question 24

Options that can be priced by considering only the payoffs at expiration are called path-independent.

Question 25

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

Question 26

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

Question 27

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?

A)7.88
B)3.38
C)4.00
D)5.00
E)1.65

Question 28

The binomial model assumes that investors are risk neutral.

Question 29

If there is one period remaining and no possibility of the option expiring in-the-money,the hedge ratio will be zero.

Question 30

The hedge ratio is the number of shares per call in a risk-free portfolio.

Question 31

Which of the following statements about the binomial model is incorrect?

A)it converges to the Black-Scholes-Merton model
B)it can accommodate early exercise
C)it allows only two stock prices at expiration
D)it can be extended to a large number of time periods
E)none of the above

Question 32

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.

Question 33

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.

Question 34

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.

A)1.22
B)1.48
C)1.40
D)1.32
E)none of the above

Question 35

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

Question 36

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

Question 37

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

Question 38

Which of the following statements about the binomial option pricing model is not always true?

A)it can capture the effect of early exercise
B)it can accommodate a large number of possible stock prices at expiration
C)it reflects the effects of the stock price,exercise price,risk-free rate,volatility and time to expiration
D)it gives the price at which the option will trade in the market.
E)none of the above

Question 39

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

Question 40

The binomial probabilities are probabilities if investors were risk neutral.

Question 41

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.

Question 42

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

Question 43

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.

Question 44

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.

Question 45

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

Question 46

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.

Question 47

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

Question 48

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

Question 49

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

Question 50

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