- CFA Exams
- CFA Level I Exam
- Topic 7. Derivatives
- Learning Module 10. Valuing a Derivative Using a One-Period Binomial Model
- Subject 1. Binomial Valuation of Options
CFA Practice Question
Assume a stock price is $55 and that in the next year it will either rise by 20% or fall by 16%. The risk-free interest rate is 5%. A call option on this stock has an exercise price of $60. What is the price of a call option that expires in one year?
Correct Answer: $3.33
π = (1.05 - 0.84) / (1.2 - 0.84) = 0.5833
S+ = 55 x 1.2 = $66
S- = 55 x 0.84 = $46.2
c+ = Max (0, 66 - 60) = $6
c- = Max (0, 46.2 - 60) = $0
c = (0.5833 x $6 + 0.4167 x $0) / 1.05 = $3.33
We have μ = 1.2 and d = 0.84
π = (1.05 - 0.84) / (1.2 - 0.84) = 0.5833
S+ = 55 x 1.2 = $66
S- = 55 x 0.84 = $46.2
c+ = Max (0, 66 - 60) = $6
c- = Max (0, 46.2 - 60) = $0
c = (0.5833 x $6 + 0.4167 x $0) / 1.05 = $3.33
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