1.1. Plot the daily futures price and price change, respectively, and comment on the price movement. Estimate and report the basic statistics (with respect to the first four moments) of the price changes.

1.2. Assume that daily futures price changes are normally distributed with zero mean. Based on the estimated standard deviation of daily price changes, suppose the exchange wants to set the margin requirement for a long position in the commodity futures so that it is 99% certain that the margin will not be wiped out by the daily price moves. How high does the margin have to be? Provide an economic intuition for your choice.

1.3. Use the data to determine how often the daily price moves would wipe out your margin. Plot the daily balance of your margin account and explain the result in your own words.

1.4. What do your results suggest about the appropriateness of the normal distribution assumption?

1.5. Suppose that the maintenance margin is equal to 75% of the initial margin calculated. How frequently would you face margin calls?

1.6. Assume you can withdraw the balances in excess of the initial margin, how frequently would your account balance with a long position be negative immediately before a margin payment is due (so that you have an incentive to default)?

1.7. Based on your analysis above, provide policy implications on what the exchange should consider when managing the default risk of futures trading for different commodit

Brent Oil

84.33

85.08

85.82

84.61

85.53

85.99

86.40

84.58

84.32

84.38

84.71

84.72

81.99

80.54

82.74

83.43

84.78

82.64

82.87

82.17

82.05

82.43

80.28

81.24

78.89

79.70

82.31

82.25

82.22

72.72

73.44

70.57

68.87