Suppose that copper costs $3 today and the continuously compounded lease rate for copper is 5%. The continuously compounded interest rate is 10%. the copper price in 1 year is uncertain and copper can be stored costlessly.
a. If you short-sell a pound of copper for 1 year, what payment do you have to make to the copper lender? Would it make sense for a financial investor to store copper in equilbrium?
b. Show that the equilibrium forward price is $3.154.
c. In what sense is $3.316 (= 3 x e^.10) a maximum possible forward price?
d. Explain the circumstances in which any price below $3.316 could be the observed forward price, without giving rise to arbitrage. (Be sure to consider the possibility that the least rate may not be 5%.)