Question 4. A stock that pays no dividends has price today of 100. In one years time the stock is worth 110 with probability 0.75 and 85 with probability 0.25. The one-year annually compounded interest rate is 5%.

a) Calculate the forward price of the stock for a forward contract with maturity one year.

b) Calculate the price of a one-year European put option with strike 100.

c) Suppose you observe that the put option in part (b) has a market price of 4. Determine an arbitrage portfolio and calculate how much profit is generated at time T = 1 by this portfolio