Problem 3 (20 pts)
An investor shorts a futures contract today to hedge the value of an asset over the next two days
(day 1 and day 2). The maintenance margin of the investor's margin account is \$1,500, which is
75% of the initial margin. The balance in the margin account at the end of today is \$1,600. If the
investor receives a margin call, the investor tops up the margin account to
at the end of the next day. The investor does not withdraw any balance in the margin account in
excess of the initial margin. What is the probability that the investor has a negative balance in the
margin account on day 2 assuming that daily settlement price changes are normally distributed
with mean 1,000 and standard deviation \$2,000? Note that in this case the investor is tempted to
walk away instead of closing out the position.