I need help with questions 1-4. I don't understand how to do these problems on his scale. The problems we do in class are done by hand and these are done with excel and I just don't understand what he is asking half the time.

EBF 473-Fall 2017 Homework 4 Due Thursday November 2 Don't forget to have at least 50 data points on all your graphs and show your work! 1) (15 points) The price of Shell stock is 200. You own one call option and one put option \"at the money\" (that is, at a price of 200). The interest rate is 4% and the time to expiration is nine months. Graph on the same graph the value of the call and the put as the standard deviation of Shell stock goes from 10 to 40 percent. (So that is two lines on the graph.) 2) (35 points) Exxon stock sells for $90/share. The annual interest rate is 2%, and the annual standard deviation on Exxon stock is 15%. The time to expiration of all options is 6 months. You are short 200 put options on Exxon with a strike price of 88. To hedge you position, you can buy or sell Exxon stock, or call options on Exxon with a strike price of 93. Given all this: A: (6 points) Derive the position you will take if you want to delta hedge your position. B: (9 points) Derive the position you will take if you want to delta-gamma hedge your position. C: (20 points) Given your answers in A and B, graph (on the same graph) the net gain or loss in your positions if the price of Exxon jumps to X, X a number between 70 and 110. (So you'll want two lines on your graph, one with the return to delta hedging and one with the return to delta-gamma hedging.) 3) (35 points) At the close of business on October 19, Chevron sold for 118.81 per share. At that time, call options at various strike prices expiring December 15 sold for the following prices: Strike 100 105 110 115 120 125 130 Price 18.65 13.47 8.90 4.68 1.67 0.415 0.075 Draw the smile for this set of call options, using the M-K technique. The interest rate is 2 percent per year. 2) (15 points) For each of four consecutive 9 month periods, starting October 19, 2014, derive the historical annual standard deviation for Chevron stock. (A hint:: treat every day as if it is has the same probability of occurring. Calculate the percentage changes each day. Then apply the formula for standard deviation across the data.)