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!)

A: Derive the position you will take if you want to delta hedge your position.

B: Derive the position you will take if you want to delta-gamma hedge your position.

C: 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 35 and 65. (So youll want two lines on your graph, one with the return to delta hedging and one with the return to delta-gamma hedging.) A hint:

D: (5 points) Using the method you employed to answer Part C, show that if the value of X is 50, there will be no change in the value of your position.