We consider a binomial model with two periods and one risky asset. The interest rate is 5%. The market evolves as follows. The risky asset has value 30 at time 0, and will go up to 60 with probability 20% and go down to 20 with probability 80% at time 1. Further, If the price was 60 at time 1, it will go up to 80 with probability 30% and go down to 40 with probability 70% at time 2. If the price was 20 at time 1, it will go up to 40 with probability 50% and go down to 10 with probability 50% at time 2. 1. What is the price of a forward contract with maturity at time 2 ? [3 points] 2. Which one of the following is closest to the price of a futures contract with maturity at time 2 ? (a) 30 ; (b) 33 ; (c) 35, why ? [3 points] 3. What is the price of a European call option with maturity at time 2 and strike 50 ? [6 points] 4. What is the price of a European put option with maturity at time 2 and strike 50