Fundamentals of Derivatives Markets (McDonald)
Chapter 10 Binomial Option Pricing
10.1 Multiple Choice Questions
1) 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
2) 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
3) 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
4) 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
5) 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
6) 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
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
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 Suudu?
A) $74.08
B) $94.24
C) $100.17
D) $111.12
9) 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
10) 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
11) 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
12) 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
13) 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
14) 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
15) 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
16) 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
17) Which number of binomial periods is most likely to produce the most accurate price?
A) 1
B) 2
C) 3
D) 4
18) 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
19) 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 %
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 %
10.2 Short Answer Essay Questions
1) 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
2) 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
Answer:
3) 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
4) Using a binomial tree explanation, explain the situation in which an American option would
alter the pricing of an option.
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5) Explain the impact a constant dividend yield would have on the price of a call option.
10.3 Class Discussion Question
1) 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.