Question

The price of a share of stock is currently $50. The stock does not pay any dividend. At the end of three months it will be either $60 or $40. The risk-free interest rate is 5% per year. An investor buys a European put option with a strike price of $50 per share. Assume that the option is written on 100 shares of stock. What stock position should the investor take today so that she would hold a riskless portfolio if it was combined with the long put option position

Answer 1

Put Delta=(MAX(50-60,0)-MAX(50-40,0))/(60-40)=-0.50000000
Buy or Long -Delta*100 shares=-(-0.5)*100=50 shares