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Question of the Week - Derivatives

AdaptPrepAdaptPrep Des Moines, IA, USAPosts: 211 Sr Associate
edited July 2015 in Level 1 Questions
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:

Question of the Week - Derivatives 18 votes

$5
27%
fabiangstylesamyakjaroliRichie321ferocious 5 votes
$6
0%
$7
72%
hairyfairyAdaptPreprsparksThomasWArsenalFanarhelpaYannickTKevinJDP1845Roman RimshakevtivTheClawMrTsotne 13 votes

Comments

  • AdaptPrepAdaptPrep Des Moines, IA, USAPosts: 211 Sr Associate
    $7

    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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