Explanation:
This question calculates the value of a call option using a three-step binomial tree:
Given:
$75$90Calculations:
Ending stock prices:
$75 × 1.2 × 1.2 × 1.2 = $129.60$75 × 1.2 × 1.2 × 0.83 = $89.64$75 × 1.2 × 0.83 × 0.83 = $62.00$75 × 0.83 × 0.83 × 0.83 = $42.89Only S_uuu is in-the-money (129.60 > 90) Probability of 3 up moves = 60%^3 = 21.6% Option value = (129.60 - 90) × 21.6% × e^(-5%×3) = 7.36
The correct answer is D based on the solution provided.
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u = e^(σ√Δt) = e^(18.25%×√1) = 1.2 d = e^(-σ√Δt) = 0.83
Next, we project the various paths the stock's price can follow over the 3 year period. The stock has 4 potential ending values:
S_uuu = $75 × 1.2 × 1.2 × 1.2 = $129.60
S_uud = S_duu = S_udu = $75 × 1.2 × 1.2 × 0.83 = $89.64
S_udd = S_dud = S_ddu = $75 × 1.2 × 0.83 × 0.83 = $62.00
S_ddd = $75 × 0.83 × 0.83 × 0.83 = $42.89
The only point at which the option finishes in the money is after 3 upward moves, with a probability of 60%^3 = 21.6%.
The value of the option today is therefore (129.60 – 90) × 21.6% × e^(-5%×3) = 7.36.
A
Not provided in the text
B
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C
Not provided in the text
D
Not provided in the text
E
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F
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