1. A stock is currently worth 80. Each year it goes up by 50% or down by 25%, with equal probability. The interest rate compounded annually is 5% (i.e., the accumulation factor for one year (one step) investment is = 1.05).

a) Find the no-arbitrage price of a 2-year European call option with strike price 80 by using the principle of risk-neutrality.

b) Find the no-arbitrage price of a 2-year European put option with strike price 80 by using the principle of risk-neutrality.

c) Using the principle of risk-neutrality find the no-arbitrage price of a 5-year binary call option with strike price K = 100 and a fixed payment of 1. At time t = 5 the option pays 1, if S(5) K, and it pays nothing otherwise, i.e. if S(5) < K.

d) Find E(S(4)), the expected value of the stock after 4 years.