1. (50) Before being delisted in 2011, one of the most famous, if least traded, derivatives was the iconic pork belly futures contract, devised to help meat packers reconcile volatility in hog prices with the seasonal variations in demand for bacon. Although now relegated to a footnote in history, pork belly futures represent perhaps the most striking intersection between the high tech, big money world of finance and the everyday needs of the average consumer. < Suppose that Becky buys futures contracts for 40, 000 pounds of frozen pork bellies from Stan, maturing 20 days from now, at a price of 1 per pound. Both the are required to post initial margins of 2000 and maintain a value of at least 1500. If a margin account falls below the maintenance requirement, the trader is subjected to a margin call and must bring the value of the account back up to 2000. < (a) (10) Suppose that the futures price followed a random walk, where < logFt+1=log Ft + t+1, ~ Et+1 N(0,0.02). < Simulate the movements of the futures price until maturity and plot the price chart. < (b) (10) Find the value of Becky's and Stan's margin accounts at the beginning and end of each day. Assume that, in the event of a margin call, both will always post the necessary funds. < (c) (10) Calculate the total payoffs to Becky and Stan. What price did Becky end up paying for the pork bellies? < (d) (10) Suppose that Becky decides that she doesn't want the pork bellies after all, and Stan does not want to arrange delivery. What will the traders do, and what payoffs do they receive? (e) (10) What returns were Becky and Stan able to attain through trading on margin? How does this compare to how much the futures price actually moved in this time frame?