Question

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.

Answer 1

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