Problem 1 (7 points) Suppose that the price today (t0 of a stock S is 50. There are four periods and you know that in each period the price can go up by 20% or down by 20%. 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 timet returns 1.05 at time(t1)) I. 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 42 that matures at date t 1? Use the binomial option pricing model (Lecture 12) to derive the price of this option at time0? (Hint: you need to replicate the payoff of the option with a portoflio based on the bank account and the stock) 3. What are the possible payoffs of a call option with strike price of 42 that matures at date 4? what is the price of this option at date 0? (Hint: you need to find the price of the option at each node of the tree att 3, t 2,t 1, andt0) 4. Plot the price of the option as a function of the price of the stock, at time t 4, Problem 1 (7 points) Suppose that the price today (t0 of a stock S is 50. There are four periods and you know that in each period the price can go up by 20% or down by 20%. 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 timet returns 1.05 at time(t1)) I. 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 42 that matures at date t 1? Use the binomial option pricing model (Lecture 12) to derive the price of this option at time0? (Hint: you need to replicate the payoff of the option with a portoflio based on the bank account and the stock) 3. What are the possible payoffs of a call option with strike price of 42 that matures at date 4? what is the price of this option at date 0? (Hint: you need to find the price of the option at each node of the tree att 3, t 2,t 1, andt0) 4. Plot the price of the option as a function of the price of the stock, at time t 4