- CFA Exams
- CFA Level I Exam
- 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 30% or fall by 20%. The risk-free interest rate is 5%. A call option on this stock has an exercise price of $60. It is selling for $5 in the market. How would you execute an arbitrage transaction to take advantage of this situation?

A. Sell the option and buy the underlying.

B. Buy the option and sell the underlying.

C. There is no arbitrage opportunity in this case.

**Explanation:**We need to calculate the price of the call option.

μ = 1.3 and d = 0.8

π = (1.05 - 0.8) / (1.3 - 0.8) = 0.5

S

^{+}= 55 x 1.3 = 71.5

S

^{-}= 55 x 0.8 = 44

c

^{+}= Max (0, 71.5 - 60) = 11.5

c

^{-}= Max (0, 44 - 60) = 0

c = (0.5 x 11.5 + 0.5 x 0) / 1.05 = 5.48

As the option is under-priced, we should buy the option and sell the underlying to replicate a loan that would charge us less than the risk-free rate.

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