CFA CFA Level 1 Question of the Week – Derivatives

Question of the Week – Derivatives

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  • AdaptPrep
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    You are interested in purchasing a 1-year call for Unic Technology at a strike price of $80. The stock is currently selling for $70; a 1-year put for Unic at $80 is worth $15. The risk-free interest rate is 3%, and the yield on Unic’s 1-year senior bonds is 5%. The price of the call should be closest to:

    • $5
    • $6
    • $7
    AdaptPrep
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    A synthetic call can be created with a long put, long stock,
    and short bond.

    We are given:

    • P0 = $15 (put price at time 0)
    • S0 = $70 (stock price at time 0)
    • X = $80 (strike price)
    • r = 3% (risk-free rate)
    • T = 1 (1 year)

    Plug this into the synthetic call formula (derived from
    put-call parity):

    C0 = P0 + S0 – X / (1 + r)^T

    = 15 + 70 – 80 / (1 + 0.03)^1

    = $7.33

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