Exercise 1 A time value of an investment follows a binomial model where the one step return rate for each time period has the possible values 5% and 2% with corresponding probabilities 0.35 and 0.65 respectively. 1) Find the value both mean and variance for the time value after 4 time periods where the beginning value of investment equals to 14 S 2) Write a computational simulation to implement the required of item 1 without depending on the mathematical relation Exercise 2 A time value of an investment follows a binomial model where the maximum and minimum of investment after 5 time periods are 35 and 20 respectively where 18 is the beginning time value. Find the average value of investment after 4 time periods where 0.4 is the probability of the one step return rate maximum 3. Fun with Reductions. (15 points) Suppose the economies of the world use a set of currencies C,..., C; think of these as dollars, pounds, Bitcoin, etc. Your bank allows you to trade each currency C, for any other currency C, and finds some way to charge you for this service. Suppose that for each ordered pair of currencies (C, C;), the bank charges a flat fee of fij >0 dollars to exchange C; for C; (regardless of the quantity of currency being exchanged). Describe an algorithm which, given a starting currency C,, a target currency Ct, and a list of fees fij for all i, j = {1,..., n}, computes the cheapest way (that is, incurring the least in fees) to exchange all of our currency in C, into currency C. Also, justify the its runtime. [We are expecting a description or pseudocode (either is OK) of your algo- rithm, as well as a brief justification of its runtime. You can use any algorithm we have learned in class.] 1. In a one-period binomial model with h = 14, the current price of a non-dividend paying stock is 50, u = 1.2, d = 0.8, and the continuous interest rate is 2%. Consider a contingent claim (i.e. an option) on the stock that pays 20 at time h if the market is up, and 7 if the market is down. a. Write out the one-period binomial stock tree for S b. Find p*. c. Find the (time 0) price C, of this option.