I am looking for help with quantitative fin risk management statistics course. I have several questions to work through. Can someone look at this one (and one other listed separately).

Instructions: . Work individually or in groups of 2 on this assignment. Submit one assignment per group. . All results/answers/discussion should be contained in the hardcopy submitted for grading. Any spreadsheets or computer programs used to generate the results should be uploaded to dropbox. . Clarity, style, and presentation will count for a portion of the assignment grades. 1. Suppose that a non-dividend-paying stock's initial price is $50, and suppose that the time-T stock price is 40 with probability 15 with probability ST 50 with probability 55 with probability with probability 10 (a) Compute the cdf and quantile function for the future stock price. (b) Plot the quantile function. (c) Suppose the set of risk-neutral probabilities is (91, 92, 43, 94, 95) = (10: 10: 10: 10: 10) is, the risk-neutral probability that Sy = 40 is q1, the risk-neutral probability that S = 45 is q2, etc. Furthermore assume that the risk-free rate of interest is 5%, so that $1 invested today grows to $1.05 at time 7. Compute i. the price of a European call option written on this stock with strike price $56 that matures at time T. ii. the initial cost of a portfolio that is long one share and short one call option (this is a covered call position). (d) Simulate 1,000 time-T stock prices (do NOT use the risk-neutral probabilities for the simulation) and convert these to simulated profit values of the i) long 1 share; and ii) covered call positions. Using the simulated values i. make histograms of the simulated profits and briefly compare. ii. estimate the expected return, standard deviation of returns and hence the risk- adjusted returns for each of the two portfolios. (e) In this case, would you decide to hedge the long stock position by writing a covered call? Briefly justify your decision