The author's website (www.rotman.utoronto.ca/ hull/data) contains daily closing prices for crude oil and gold futures contracts. 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 daily price movement that will not be exceeded with \(99 \%\) confidence.

(b) Suppose that an exchange wants to set the maintenance margin for traders 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 the margin calls are made at the end of a day and the trader has until the end of the next day to decide whether to provide more margin.) How high does the margin have to be when the normal distribution assumption is made?

(c) Suppose that the maintenance margin is as calculated in (b) and is \(75 \%\) of the initial margin. How frequently would the margin have been wiped out by a two-day price movement in the period covered by the data for a trader with a long position? What do your results suggest about the appropriateness of the normal distribution assumption?