- CFA Exams
- CFA Exam: Level I 2021
- Study Session 16. Derivatives
- Reading 49. Basics of Derivative Pricing and Valuation
- Subject 11. Binomial Valuation of Options

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**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

S

c

c

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 = $66S

^{-}= 55 x 0.84 = $46.2c

^{+}= Max (0, 66 - 60) = $6c

^{-}= Max (0, 46.2 - 60) = $0c = (0.5833 x $6 + 0.4167 x $0) / 1.05 = $3.33

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