The author’s website (www-2.rotman.utoronto.ca/~hull/data) contains daily closing prices for the crude oil futures contract and the gold futures contract. You are required to download the data for crude oil and answer the following:

(a) Assuming that daily price changes are normally distributed with zero mean, estimate the standard deviation of daily price changes. Calculate the standard deviation of twoday changes from the standard deviation of one-day changes assuming that changes are independent.

(b) Suppose that an exchange wants to set the margin requirement for a member with a long position in one contract so that it is 99% certain that the margin will not be wiped out by a two-day price move. (It chooses two days because it considers that it can take two days to close out a defaulting member.) How high does the margin have to be when the normal distribution assumption is made? Each contract is on 1,000 barrels of oil.

(c) Use the data to determine how often the margin of the member would actually be wiped out by a two-day price move. What do your results suggest about the appropriateness of the normal distribution assumption?

(d) Suppose that for retail clients the maintenance margin is equal to the amount calculated in

(b) and is 75% of the initial margin. How frequently would the balance in the account of a client with a long position be negative immediately before a margin payment is due (so that the client has an incentive to default)? Assume that balances in excess of the initial margin are withdrawn by the client.