Question

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

Answer 1

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