Question

# The price of a European call on a stock that expires in one year and has...

The price of a European call on a stock that expires in one year and has a strike of \$60 is \$6. The price of a European put option on the same stock that also expires in one year and has the same strike of \$60 is \$4. The stock does not pay any dividend and the one- year risk-free rate of interest is 5%. Derive the stock price today. Show your work.

We can use put-call parity equation to calculate the stock price today in following manner

C + K* e^ (-r*t) = P + S0

Where,

C = price of the European call option =\$6

P = price of the European put option =\$4

S0 = current stock price =?

Strike price K= \$60

The risk-free rate r= 5%

Time period t= 1 year

Now putting all the values in the put-call parity equation, we get

\$6 + \$60 * e^ (-0.05*1) = \$4 + S0

Or S0 = \$6 + \$60 * e^ (-0.05*1) - \$4

Or S0 = \$6 + \$57.07 - \$4 = \$59.07

Therefore the stock price today is \$59.07

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