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Suppose that the price today (t = 0) of a stock S is 60. There are four periods and you know that in each period the price can go up by 25% or down by 25%. In each peridod you also have access to a bank account, which pays a constant an interest of 5% (a dollar invested in the bank account at time t returns 1.05 at time (t + 1)). 1. Find the stock price tree up to date t = 4. 2. What are the possible payoffs of a call option with a strike price of 55 that matures at date t = 1? Use the binomial option pricing model (Lecture 14) to derive the price of this option at time t = 0. What happens with the price of the option at time t = 0 if the strike price is instead 50? 3. What are the possible payoffs of a call option with strike price of 55 that matures at date t = 4? What is the price of this option at date t = 0? (Hint: you need to find the price of the option at each node of the tree at t = 3, t = 2, t = 1, and t = 0) 4. Plot the value of the option with strike price 55 as a function of the price of the stock, at time t = 3 and t = 4