1. Consider a two period (t=0,1,2) world where the stock of ABC Company is selling for $90 at t=0. In every period, which is six months long, the stock price can either increase or drop by 20% or drop by 20%. The market is offering European options on this stock with strike price $85 and a government-issued zero-coupon bond, all maturing one year from now. The bond is selling for $956 at the present. Assume that interest rates remain constant through time. 1.1. Compute the risk-neutral probabilities of the states of the market in a oneyear time. 1.2. Design a strategy in this setting that will ensure that portfolio remains risk-free in every subsequent point in time. That is, explain in detail what trades must be made at each point in space-time, to achieve that. 1.3. Compute the prices of European call and put options in this setting. 1.4. Suppose at time t=2 the owners of the stock are to receive dividends in the amount of d dollars per share of stock. For which values of d will an American call option be exercised at time t=1?