3. (20 points) Consider the binomial tree model. Suppose the stock price at time zero is S0, and the stock does not pay dividends. The risk free rate is r and the time step is t. Consider an exotic option with present time 0 and the maturity at time T = Nt and the payoff at the maturity is (S1) 2 + (S2) 2 + + (SN ) 2 . What is the time 0 price of this option?