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 oneyear risk-free rate of interest is 5%. Derive the stock price today. Show your work.

Answer 1

If both the options (call and put) are on the same underlying stock with same strike price and maturity, put-call parity is used to arrive at the stock price.

Put call parity is nothing but value of a fiduciary call (long call (Co), plus an investment in the zero-coupon bond with a face value equal to strike price (X)) is equal to Protective put (long stock (Stock price=So) and long put(Po))

It comes in this way, Co+PV(X)= So+Po

So=Co-Po+PV(X)

So=$6-$4+(X/(1+rf)^T)

rf= risk free rate of return=5% and T is maturity= 1year

So=$2+($60/(1.05)^1)

So=$2+($57.14)

So=$59.14

Hence the stock price =$59.14