Deck 10: Binomial Option Pricing: Basic Concepts

Question 1

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

Answer 1

B

Question 2

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

Answer 2

The value of an American option at a node is the maximum of its intrinsic value or the discounted value of the subsequent nodes.Early exercise permits the realization of the intrinsic value,should it be the higher number.European options may not consider this potential gain.

Question 3

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

Answer 3

B

Question 4

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 5

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 6

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

Question 7

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 8

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 9

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 10

The monthly standard deviation for a stock is 4.2%.What is the 6 month standard deviation for the security?

A) 4.2 %
B) 10.3 %
C) 25.2 %
D) 50.4 %

Question 11

The stock price in KMW,Inc.is $50,$54,$56,and $48 on four consecutive days of trading.What is the continuously compounded return on the stock over this time frame?

A) -3.85 %
B) -4.00 %
C) -4.08 %
D) -4.16 %

Question 12

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 cannot be determined

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

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 Sᵤᵤdᵤ?

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

Question 15

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 16

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 17

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 18

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 19

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 20

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

Question 21

Discuss options on other assets.Ask students to define currency options,futures options,index options,and commodity options.Require that the students state which variables in the securities listed above correspond with the binomial pricing inputs used for stock options.