University of Connecticut
Math 3615: Financial Mathematics Problems
Spring 2009
4/14/09 Examples – Module 12
1. The current price of an index is S
0
= 1,000.
The 6-month forward price for the index is 1,025.
The continuously-compounded annual risk-free interest rate is r = 0.06
The continuous annual dividend yield for this index is
δ
= 0.02.
(a) Based on the above information, you detect an arbitrage opportunity. What
positions can you take in the index, in a 6-month forward contract for the index,
and in a 6-month risk-free bond so that you have no exposure to changes in the
value of the index, have no out-of-pocket cost, and will realize a profit at the end
of 6 months?
(Assume that the stock, the bond, and the forward contract are all available in
non-integer amounts (i.e., fractional units).)
(b) What is the amount of your profit from this arbitrage (measured as of the end of
the year)?
