You are given the following alternative for a EUR 7,800 investment: either invest in a stock, whose price is S = EUR 26 per share, or buy 3-month call options, Strike price X = EUR 30, that costs C = EUR 6 per option. What stock price at maturity would make both alternatives equivalent
Let the stock price at maturity be X.
Profit from call option = [ stock price - exercise price ] - premium
Now the number of shares that can be purchased from Eur 7800 = 7800 / 26 = 300
Now number of options that can be purchsed from Eur 7800= 7800 / 6 = 1300
Now to make investment value equal
300 X - 7800 = (X -30 ) * 1300 - 7800
300 X -7800 = 1300 X -39000 -7800
39000 = 1300X - 300X
X = 39000 / 1000 = 39
stock price at maturity that would make both alternatives equivalent = 39
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