Deck 10: Binomial Option Pricing

Question 1

For an option trading in the money, what is the likely impact on the binomial option price as the number of binomial steps is increased?

A) The price will fall
B) The price will increase
C) The price will remain constant
D) The impact can not be determined

Answer 1

A

Question 2

What is the binomial option price assuming the following data on a 6-month call option, using 3-month intervals as the time period? K = $40, S = $37.90, r = 5.0%, = .35

A) $ 2.05
B) $ 2.10
C) $ 2.96
D) $ 3.08

Answer 2

D

Question 3

Assume the following data on a 6-month put option, using 3-month intervals as the time period. K = $40.00, S = $37.90, r = 5.0%, = .35. What is the binomial option price?

A) $ 2.10
B) $ 2.86
C) $ 3.91
D) $ 4.25

Answer 3

C

Question 4

Which number of binomial periods is most likely to produce the most accurate price?

A) 1
B) 2
C) 3
D) 4

Question 5

A stock is selling for $18.50. The strike price on a call, maturing in 6 months, is $20. The possible stock prices at the end of 6 months are $22.50 and $15.00. Interest rates are 6.0%. How much money would you borrow to create an arbitrage on a call trading for $2.00?

A) $2.54
B) $4.85
C) $6.60
D) $8.85

Question 6

Using a binomial tree, what is the price of a $40 strike 6-month call option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, σ = 0.35

A) $2.50
B) $2.76
C) $2.92
D) $3.08

Question 7

A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over 6 months, assuming two periods of 3 months each?

A) $64.96
B) $69.69
C) $73.48
D) $76.96

Question 8

A stock is selling for $68.50. Interest rates are 6.0% and the returns on the stock have a standard deviation of 32.0%. What is the forecasted price of the stock using 3-month periods at S_uudu?

A) $74.08
B) $94.24
C) $100.17
D) $111.12

Question 9

In the case of a 1-year option, the current stock price is $52 per share. If the stock price has an equal chance of ending the year at either $58 or $45, what is the △ given an interest rate of 6.0% and an exercise price of $50?

A) 0.2145
B) 0.3254
C) 0.5411
D) 0.6154

Question 10

Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $50, S = $48, r = 4.0%, = .27. What is the highest expected stock price after 3 months according to the binomial model?

A) $ 48.00
B) $ 50.00
C) $ 55.56
D) $ 59.27

Question 11

Compute Δ for the following call option. The stock is selling for $23.50. The strike price is $25. The possible stock prices at the end of 6 months are $27.25 and $21.75.

A) 0.4091
B) 0.6822
C) 0.8433
D) 0.9216

Question 12

Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $50, S = $48, r = 4.0%, = .27. What is the risk neutral probability of an up move in the stock price?

A) 45.24 %
B) 47.25 %
C) 52.75 %
D) 54.76 %

Question 13

A stock is selling for $41.60. The strike price on a call, maturing in 6 months, is $45. The possible stock prices at the end of 6 months are $35.00 and $49.00. Interest rates are 5.0%. Given an under-priced option, what are the short sale proceeds in an arbitrage strategy?

A) $6.36
B) $8.22
C) $10.43
D) $11.89

Question 14

Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $70, S = $68.50, r = 6.0%, = .32. What is the highest possible stock price associated with this data and the binomial pricing model?

A) $ 51.26
B) $ 68.50
C) $ 70.59
D) $ 91.21

Question 15

A call option has an exercise price of $30. The stock price at a point on the binomial tree is $36.24. The calculated present value of the option at that same point is $5.86. What figure should be used to calculate option prices at points moving toward the final price?

A) $5.86
B) $6.24
C) $6.62
D) $7.01

Question 16

A stock is selling for $32.70. The strike price on a call, maturing in 6 months, is $35. The possible stock prices at the end of 6 months are $39.50 and $28.40. If interest rates are 6.0%, what is the option price?

A) $1.90
B) $2.80
C) $3.40
D) $4.20

Question 17

Using a binomial tree, what is the price of a $40 strike 6-month put option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, σ = 0.35

A) $3.52
B) $3.66
C) $3.84
D) $3.91

Question 18

A stock is currently selling for $22.00 per share. Ignoring interest, determine the intrinsic value of a call option should there exist equally probable stock prices of $25.00 and $23.00.

A) $0.00
B) $1.00
C) $2.00
D) $3.00

Question 19

A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over a 6- month interval?

A) $64.96
B) $69.69
C) $73.48
D) $76.96

Question 20

For a specific futures option, given d = .813 and u = 1.367, what is the risk neutral probability of an up move in the price of the option?

A) 41.87 %
B) 43.54 %
C) 47.98 %
D) 56.46 %

Question 21

Using a binomial tree explanation, explain the situation in which an American option would alter the pricing of an option.

Question 22

Draw the binomial tree listing only the stock prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $70, S = $68.50, r = 6.0%, σ = 0.32

Question 23

Explain the impact a constant dividend yield would have on the price of a call option.

Question 24

Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month put option, using 3-month intervals as the time period. K = $40.00, S =
$37.90, r = 5.0%, σ = 0.35

Question 25

Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $40, S =
$37.90, r = 5.0%, σ = 0.35