Please include all work and steps with brief explanations. Also include a table and graph with at least 50 data points. Thank you.

2) (75 points) Walmart stock sells for $50/share. The annual interest rate is 2%, and the annual standard deviation on Walmart stock is 24%. The time to expiration of all options is 6 months. You are short 90 call options on Walmart with a strike price of 48. To delta hedge your position, you can buy or sell Walmart stock. To delta-gamma hedge your position, you can use Walmart stock and a put option on Walmart at 53. (Be careful with your delta on the put option!) Given all this: A: (15 points in total) Derive the position you will take if you want to delta hedge your position. B: (20 points) Derive the position you will take if you want to delta-gamma hedge your position. C: (40 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 Walmart jumps instantaneously to X, X a number between 38 and 68. (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.) A hint: If the value of X is 50, there will be no change in the value of your position. 2) (75 points) Walmart stock sells for $50/share. The annual interest rate is 2%, and the annual standard deviation on Walmart stock is 24%. The time to expiration of all options is 6 months. You are short 90 call options on Walmart with a strike price of 48. To delta hedge your position, you can buy or sell Walmart stock. To delta-gamma hedge your position, you can use Walmart stock and a put option on Walmart at 53. (Be careful with your delta on the put option!) Given all this: A: (15 points in total) Derive the position you will take if you want to delta hedge your position. B: (20 points) Derive the position you will take if you want to delta-gamma hedge your position. C: (40 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 Walmart jumps instantaneously to X, X a number between 38 and 68. (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.) A hint: If the value of X is 50, there will be no change in the value of your position