Derive a Theoretical Price for Each of the Following Futures

Essay

Derive a theoretical price for each of the following futures contracts quoted in the United States and indicate why and how the market price should deviate from this theoretical value. In each case, consider one unit of underlying asset. The contract expires in exactly three months, and the annualized interest rate on three-month dollar London InterBank Offered Rate (LIBOR) is 12%.
All interest rates quoted are annualized.
$\begin{array}{c}\begin{array}{lll} \text {Contract}\\ \text {a. Gold Futures:}\\\\ \text {b. Currency Futures:}\\\\ \text {c. Eurodollar Futures: (3-month \( \$ \) LIBOR):}\\\\ \text {d. Stock Index Futures:}\\\\\end{array}\begin{array}{lll} \text {Useful Information}\\ \text {Spot gold price=\$ 300 per ounce; cost of storage= }\\ \text { \$ 0.50 per ounce per month}\\ \text {\$ / € spot exchange rate =1.10dollars per euro; }\\ \text {3-month euro interest rate =4 \% }\\ \text {6 -month \$LIBOR interest rate =10 \% }\\\\ \text {Current value of stock index =1,200 ; annual}\\ \text { dividend yield=2 \%} \end{array} \end{array}$