3. Problem 2.32. (Excel file) T he author's Web page (wwrotman.utorontoca/\"hull/data) contains daily closing prices for the crude oilr futures contract and gold futures contract. (Both contracts are traded on NYbl'X.) You are required to download the data and answer the following: a) b) How high do the maintenance margin levels for oil and gold have to be set so that there is a l % chance that an investor with a balance slightly above the maintenance margin level on a particular day has a negative balance two days later? How high do they have to be for a 0. l % chance? Assume daily price changes are normally distributed with mean zero. Explain why the exchange might be interested in this calculation Imagine an investor who starts with a long position in the oil contract at the beginning of the period covered by the data and keeps the contract for the whole of the period of time covered by the data. Margin balances in excess of the initial margin are withdrawn. Use the maintenance margin you calculated in part (a) for a l % risk level and assume that the maintenance margin is 75% of the initial margin. Calculate the number of margin calls and the number of times the investor has a negative margin balance and therefore an incentive to walk away. Assume that all margin calls are met in your calculations. Repeat the calculations for an investor who starts with a short position in the gold contract